Awwwwwww!!!!! Thanks Silwen, you are very kind
These are Polish/Ukrainian style "Pisanki" or decorated Easter Eggs.
The technique used with these is basically wax resist. I have a little wax wand implement (think a little wooden stick, small pencil lengh, hole at the end that holds a tiny down-pointing copper cone/funnel, strapped into place with copper wire.). I also have a blob of wax that comes in a little "cake" that looks exactly like a reese's peanut butter cup shape-wise.
You need a candle for this, and some paper towels.
You scoop up some hard wax into the cone, and warm the wand over the candle flame... then make designs on the egg with the wand (tip of the cone leaks molten wax in a thin stream). What you cover with wax will stay the colour under the wax. Then you proceed to dye the egg in various colours (the dyes are powders or tablets you dissolve in boiling water with a spoonful of vinegar, and the eggs are dipped into the jars/bowls of dye for several minutes to take up the given colour). The best dyes I have used came from a specialty Ukrainian store here...but the ones I used this year were polish and german Easter Egg dyes that I got at an all purpose European deli around Easter.
With several steps, coats of dye and re-waxing, you can get very intricate patterns. You then gently melt off the wax over a candle flame and rub off with a paper towel.
Sounds complex and its awkward to put in writing, but its really no difficult science. Takes patience and its easy to screw up, but its fun to do.