There are a few other One-handed Deck Cutting Instructables out there, but they all deal with what I'm calling the "flip version". Here is one of the better ones.

This is what I call the "spin-version".

Video is at the bottom (step four); below are images and a step-by-step guide.

p.s. the bigger your hands are, the easier it is to do this.

Step 1: Holding the Deck

Remove the jokers from the deck first (unless for whatever reason you need them shuffled in).

You should use your three middle fingers to hold the deck (i.e. not the pinky or thumb). Your ring and index fingers will be on opposite sides of the deck, putting pressure on the long sides, about halfway down. While your index and ring fingers are doing the actual holding, your middle finger basically rests against the top edge of the deck to provide stability and keep the cards even. For ease, you can also rest your thumb against the opposite side as the middle finger, but it is not necessary. Besides, you'll be moving your thumb in the next step.

Throughout this guide, remember when I say pressure, I don't mean to squeeze the cards, just hold them (like how one would hold a pencil when relaxed).

Step 2: The Thumb Sweep

(that's what I call it anyway)

Cross your thumb across the deck so that it is touching the corner below your ring finger. With your thumb, put pressure on the top half of the deck (if you are having trouble, such as grabbing too many or too few cards, try bending your thumb a bit). Your ring finger will need to put slight pressure near the top corner to provide a contrast for the thumb (this should keep the lower half of the deck from following the thumb).

Now, this is one of the more tricky parts.

With your thumb, drag the top half of the cards across in the opposite direction as earlier. Your index finger will need to do a sort of swiveling thing so that it's main joint (the lower one) maintains pressure on the lower half of the deck (along with your ring finger), and at the same time, the area between the two upper joints of the index finger puts pressure on the top half along with your thumb. In both cases, your index finger remains at the middle of the long side.

At the end of this step, the top half and bottom half of the deck should be perpendicular to each other, making an L shape.

Step 3: The Tilt and Swap

(really I just enjoy making up names for the moves)

You keep dragging the deck past the L shape. Your middle finger will now play more of a roll in holding the bottom half of the deck, and your pinky should also fold over to help hold the bottom half. At this point, your index finger all but abandons the lower half; the outside of the main knuckle is still touching it, but nearly all the pressure is on the top half.

You will now basically rotate the top half another ninety degrees (to make a full 180), As you pull the deck far enough, both halves should naturally fall into a slant, with the outside edges downward, and the inner edges upward. This should happen right as there's only a corner of the top half left over the bottom half.

Once you get that last corner over the lower half, your index finger should lose all meaningful contact at all with the lower half. It may still brush against it, but it doesn't have to, and it doesn't really help any. At the same time, your middle, ring, and pinky fingers should fold over the top of the bottom half of the deck so that it is basically cradled in those three joints.

Your thumb will still be putting pressure on the original corner it touched, and your index finger should partially fold over the top half to provide more stability. At this point, the two halves should be completely separate from each other, and the inside edges should be approximately parallel.

Now you tilt the previously-lower half of the deck to a more 45 degree angle, and you lower the previously-top half to almost flat, sliding it beneath the previously-lower half as you do so.

Now your index finger completely removes itself from the trick, your thumb pushes the previously-upper half further, and when they're about even, tilt your hand slightly, release the tension, and allow gravity to put the cards back together.

Step 4: Rinse and Repeat

It is really easy to continue cutting the deck like this when you have finished step three.
I personally, like to cut the deck like this over and over again, partially for practice, but also because it is fun and gives me something relaxing to do.

Enjoy your new flourish!
(flourishes are my favourite part about cards)

Video:

You may notice 1) that one the fourth cut, the top card stayed with the bottom of the deck. This can happen by accident because you are pressing to hard on top with your ring finger, but, you can also use it on purpose if you wanted to try a trick with it; and 2) yes, I did drop a card - sometimes it happens, as I'm not an expert.

Practice helps!