1 Make the filling: Put the apricots in a small saucepan and add enough water to cover. Put on the lid, bring to a boil, reduce the heat, and simmer until the fruit is tender, about 10-15 minutes.
Remove the apricots from the saucepan with a slotted spoon and place in a food processor. Reserve the cooking water.
Add the honey and 1 tablespoon of the cooking water to the food processor, and puree until very smooth, scraping down the sides of the food processor from time to time. If the fruit is too thick for the machine to puree it, add 1 to 2 more tablespoons of cooking water.
Scrape the filling into a container, let it cool, cover with plastic wrap, and refrigerate overnight or up to 3 days before baking.
2 Make the dough: Lay a large sheet of plastic wrap on the counter.
In a large bowl, whisk together the flour, sugar, baking powder, and salt. Using the large holes of a box grater, grate the margarine or butter into the bowl (work quickly so the butter does not melt). Add the lemon and orange zest.
Work the grated butter into the flour with a pastry cutter or your fingertips until the mixture resembles coarse cornmeal. Add the egg and knead with your hands for a minute or 2, until the dough is smooth and no longer crumbly.
Lay the dough on the plastic wrap, press into a flat rectangle, and wrap tightly. Chill in the refrigerator overnight, or up to 3 days.
3 Heat the oven and prepare the baking sheets: Preheat the oven to 400°F and position racks in the upper and lower thirds of the oven. Line 2 baking sheets with parchment paper or silicone baking mats. Take the dough out of the refrigerator and let it come to temperature for 10 minutes.
4 Roll out the dough Lightly flour your countertop. Cut the dough in half; return one half to the refrigerator.
Dust both sides of the dough lightly with flour. Roll out to an even 1/8-inch thickness. Use a dry pastry brush or your hands to brush off the excess flour. Using a 3-inch biscuit or cookie cutter or a drinking glass, cut the dough into rounds.
Place the rounds on the baking sheets as you go. Once your first sheet is filled, pop it in the fridge so the cookies keep their shape while you work on the second baking sheet. Save and refrigerate the dough scraps.
Repeat with remaining half of dough, then re-roll scraps and get as many rounds as you can out of them. (You’ll have anywhere between 26 to 36 rounds).
5 Fill the cookies: Transfer the chilled filling to a piping bag or a zip-top sandwich bag with the corner snipped off.
Working with one baking sheet at a time, pipe a circle of filling (about 1-1/2 teaspoons) on the center of each dough round. (You will likely have extra filling. Store it in the refrigerator and use it to spread on toast or stir into yogurt.)
6 Shape the cookies: Start by folding one edge over. Fold the second edge over so one corner overlaps the other and forms a 60-degree angle. Fold the third edge over, creating the three distinct corners of a triangle. The first few cookies you shape might not be perfect, but you’ll get the hang of it quickly. There is no need to press, pinch or seal the edges.
7 Bake the cookies: Arrange the cookies so they are about 2 inches apart (they should all fit on two baking sheets). Bake and set your timer for 6 minutes.
When the timer goes off, rotate the sheets front to back and top to bottom. Reset the timer, and bake the cookies for an additional 5 to 10 minutes, or until the edges are golden brown. Total baking time will be 12 to 16 minutes.
8 Cool the cookies: Cool the cookies on sheets for 2 minutes, then transfer to cooling racks with a metal spatula. You may serve the cookies warm, but they are best at room temperature.
The cookies are crispiest on the day you bake them, but they will last up to 3 days in a tightly covered container.