Preheat oven to 350°F (175°C). Grease or line a 9-inch tart pan with parchment paper.
Make the dough:In a large bowl, combine flour, baking powder, and sugar.Cut in the cold butter until the mixture resembles coarse crumbs.Make a well in the center, add eggs, vanilla, lemon juice, and zest and whisk. Start to incorporate in the dry ingredients. Then transfer to a lightly floured smooth surface and knead the dough to a smooth consistency (3-4 minutes) cover the dough and let it rest for 30 minutes for easier rolling.
Roll out dough for base:Roll out 2/3 of the dough into a circle slightly larger than 9 inches.Carefully press into the tart pan, letting the edges hang slightly over the rim.
Add the filling:Spread peach jam evenly over the dough, leaving a 1-inch border.Arrange fresh peach slices on top of the jam.
Create the lattice top:Roll out the remaining 1/3 of dough into 10 thin strips.Lay strips over the filling in a crisscross pattern.Fold the edges of the base dough over the lattice strips, pressing gently.
Bake:Brush the dough edges and lattice with a little beaten egg for a golden finish.Bake 35–40 minutes, or until crust is golden and filling is bubbly.
Cool & serve:Let the crostata cool in the tart pan for 15–20 minutes before slicing.Serve warm or at room temperature, optionally with vanilla gelato or whipped cream.