Start by boiling the eggs. I boil mine for about 15-20 minutes for a fully set yolk – no jammy centers here, you want them firm for the egg salad. While the eggs are boiling, this is the perfect time to prep the cucumber.
Use a vegetable peeler to shave the cucumber into long thin flat ribbons – just run it down the length of the cucumber over and over. A good sharp peeler makes this so easy – I use an OXO one and it works great.
Once the eggs are done, peel them and add them to a bowl with the mayo, scallions, salt, pepper, and mustard if you’re using it. Smash and mix everything together into a chunky egg salad – you don’t want it too smooth, a little texture is good.
Warm the tortillas slightly if they feel stiff – just 10-15 seconds in the microwave or a quick moment in a dry pan or in a big toaster if you have.
Spread a generous layer of egg salad over each tortilla, leaving a small border at the edges. Lay the cucumber ribbons across the salad in lines, then roll the tortilla up into one tight log.
Here’s a trick worth knowing – before you slice them, wrap the rolls in plastic wrap and put them in the fridge for 15-30 minutes. They firm up and hold their shape so much better, and you’ll get clean, beautiful rounds instead of them falling apart when you cut. If you’re in a rush you can skip this but it really does make a difference.
Slice each roll into rounds about 1 inch thick and arrange on a board or wide white platter. If you’re serving these as an appetizer, skewer one olive and one roll up together on a pearl toothpick – it looks really elegant and makes them easy to grab.