Sift flour and baking powder into a large bowl. In another bowl, whisk the eggs and sugar until combined. Whisk in milk, melted butter, salt and lemon zest until smooth. Fold the dry ingredients into wet in 2-3 additions, until well incorporated.
Finish mixing the dough with your hands and press it into a ball. If it's very sticky add another tablespoon or two of flour until it sticks together, but not more than that. The dough should be smooth and soft.
Let the dough rest in the refrigerator for 15 minutes (or even a few hours), this makes handling it easier. As you get ready to bake, preheat the oven to 350°F (175°C - see notes for more) with a rack in the center of the oven. Line two baking sheets with parchment paper and set aside.
Roll the dough into 2 logs, slice each log into into 44 pieces and shape each one into a smooth ball. Transfer them to the prepared baking sheets, placing them 1 inch (2.5 cm) apart, as they will rise during baking. Press down each ball slightly, so the bottom flattens.
Bake the first round for about 10 minutes, until bottoms are golden brown (the tops will remain pale). Rotate the pan halfway through baking. As you take the first tray of cookies out, put the second one in the oven.
While the cookies are still warm, cut a circle in the bottom of each cookie and scoop out enough of a cookie for it to hold some filling. (Be careful, don't pierce the cookie too deep or you risk breaking it.) Set the scooped out cookies aside.
Repeat the process with the second tray of baked cookies. Next, find a pair for each cookie, you want the halves of the peach to be of similar size. Choosing them at this stage is easier than finding one mid-filling.