In a large bowl combine the flour, sugar, salt, and baking powder and mix until combined.
Using a pastry cutter or your hands, mix in the butter until the mixture resembles coarse crumbs.
Add the beaten egg and lemon zest and mix until the dough is formed. It will be crumbly. Using your hands, shape the dough into a ball. If it's too dry, add a tablespoon of milk. Once the dough ball is formed, cover it with plastic wrap and refrigerate it for at least 30 minutes.
Remove the dough and allow it to rest for 10 minutes at room temperature. Preheat the oven to 350f and line two baking sheets with parchment paper. While the dough is resting, spread the sesame seeds out onto a plate and pour the milk into a shallow bowl.
Cut the dough ball into 4 equal pieces, and roll each piece into a 1/2-inch thick rope.
Cut the log into 2-inch long pieces, then lightly dip in the milk and roll in the sesame seeds until coated.
Place the cookies on the prepared baking sheets about 1 inch apart and bake for 30 minutes until golden.
Allow the reginelle to cool completely before serving. Enjoy!