Since I couldn't find anything like this, me and my dad decided to build one ourself.
This instructable does not include the complete instructions for the cabinet, but only for the part with the rounded doors since that is the most difficult part.
Step 1: Make a mold
1. Nail 2 pieces of MDF together, so both molds will be exactly the same. Make sure the nails stick out a little so you can easily remove them later on.
2. Cut them to a rectangle that is much longer and a little wider than you need.
3. On one side of the rectangle, draw a half circle. Make sure the mold will still be much wider than you really need. Draw a center line on the molds. We will need this later on for alignment.
4. Cut out the half circle a little wider than you need. You should now end up with a mold that has an approximate circle that is a little too wide.
5. Shave the mold on all 4 sides to exactly the curvature you need. Do make sure that it keeps quite a bit longer than what you actually need.
6. Remove the nails to separate the two molds. You should now have to identical molds with exactly the right curvature.
7. Nail the two molds onto a third piece of wood, making an upside-down pi shape. The two molds should be spaced apart so that they are placed at 1/4 and 3/4 of the length of the piece of wood you want to bend.
Note: the molds can be re-used later on for top and bottom part (or interior shelf). The time it takes to make these two identical is thus not only for making a one-time only mold but also for making other parts of the cabinet.