Tear apart the paper towels into small rectangles. Place a cool, dry egg in the middle of the paper towel.
Wrap the paper towel up and around the egg so it's completely covered. Twist the top of the paper towel so it's tight against the egg and secure it with a tiny hair elastic or a twist tie.
Wearing rubber gloves, gently squeeze drops of food colouring directly onto the paper towel wrapped egg (3 or 4 drops at a time), leaving some white space between each colour. Repeat until there are large food colouring dots around the whole egg.
Using a spray bottle, gently spray a small amount of water into the center of each food colouring dot. Keep spraying until the colours bleed and there is no more white space. The less water you spray, the brighter the colours on the egg will be.
Gently squeeze the wet paper towel wrapped egg over the sink to drain any excess water. Even if there's no extra water, gently squeeze the egg to make sure the colour on the paper towel transfers to the egg.
Place the wet, paper towel wrapped eggs in a baking dish. Point a table fan at the eggs and allow them to dry for 3 to 4 hours. (Without a table fan, you'll have to wait overnight for them to dry).
When the paper towels are completely dry, remove the elastics and unwrap each egg.
Notes
It's best if you can make these the day you plan to serve them. If they MUST be refrigerated, place the eggs in an egg carton. Make sure you remove them from the fridge (and open the egg carton lid) at least 3 hours before you plan to serve them to give time for the condensation to dry.