Pickled-eggs are a traditional British chip-shop & pub snack, and fairly easily made.
Here's one way of making them, using:

Fresh free-range hen's eggs (thanks to Julie)
Sarsons malt pickling vinegar
Salt
Spices
A sauce pan with a lid
A clean glass jar

Some of the photography utilises my adjustable Lego lamp

Step 1: Preparing the Eggs

Hard boil the eggs, but only just. The eggs I used this time were rather small and were cooked fairly quickly. I know my eggs, altitude & water and can usually get these just right, but it may require practice / trial & error.
If you boil eggs for too long the yolk will become pale yellow & "dry" with an ugly dark layer between it and the white. Soft-boil and the yolk will be runny.
Small eggs were placed carefully in a pan, soft-water (at about 1000 feet above sea level it boils under 100^oC) was boiled and poured into the pan. The eggs were boiled gently for ~8 min, the water removed and the hot eggs replaced in the box to cool.

I took the opportunity to clean the pan at the same time (dried-on rice) - green cleaning!

Step 2: Pickling

Having cleaned and dried the pan, I added:

Dried chillies
Cloves
Cardamon pods (split)
Black pepper (cracked)
Salt ~ 2 table spoons

To the above was added ~pint of pickling vinegar (6% acidity, also spiced). This was heated gently for ~1 hour before binging to a gently boil.
! Do this with the lid on, as vinegar-fumes are irritating to the eyes & nose.

Meanwhile the cold eggs were peeled, and added to a clean glass jar. The hot boiling vinegar was poured over the eggs, with care to avoid hot-fumes as best as practically possible.

Step 3: And Finally...

Leave for about a week, and they are done. Longer pickling will make these tougher and more highly flavoured, notice that the white eggs pick-up colour from the vinegar.
I got the yolks just right in these: generally firm, but a good yellow and still moist & soft.

Most ingredients can be changed, but it is important to use good eggs, strong vinegar and flavour. A light dusting of white pepper is good with these after you've bitten the top off (this would be done in images 2 & 3, but there was enough flavour _{and I don't have any white pepper in})