In a large bowl, whisk together the flour, granulated sugar, baking powder, salt, and lemon zest until evenly combined.
Scatter the cold cubed butter over the dry ingredients and rub it in with your fingertips or a pastry cutter until the mixture looks like coarse, sandy crumbs with a few pea-sized pieces remaining.
Make a well in the center and add the 2 egg yolks, the whole egg, and the vanilla extract. Mix with a fork, then bring the dough together with your hands until it just forms a ball. Do not overwork it.
Press the dough into a flat disc about 1 inch thick, wrap it tightly in plastic wrap, and refrigerate for at least 30 minutes.
While the dough chills, slice the peaches into 1/4-inch pieces and toss them in a bowl with the granulated sugar, cornstarch, lemon juice, and cinnamon if using. Let them sit while you roll the dough.
Preheat your oven to 375°F (190°C). Lightly flour a sheet of parchment paper and roll the chilled dough into a circle about 12 inches (30 cm) across and 1/4 inch thick.
If using a tart pan, transfer the dough into it and press gently into the corners, trimming any excess. For a free-form crostata, leave the dough on the parchment and slide it onto a baking sheet.
Spread the apricot or peach jam evenly over the base of the dough using an offset spatula, leaving a 1.5-inch (4 cm) border bare for free-form or spreading to the pan edge for a tart pan.
Lift the peach slices out of the bowl, leaving most of the excess liquid behind, and fan them over the jam in overlapping concentric circles or pile them loosely for a rustic look. Drizzle a spoonful of the remaining juices over the fruit.
For a free-form crostata, fold the bare dough border up and over the outer ring of fruit, pleating as you go. Brush the exposed dough with the egg wash and sprinkle with turbinado sugar.
Bake for 40 minutes, or until the crust is deep golden and the peach juices bubble at the edges. If the crust browns too quickly, tent the edges loosely with foil.
Let the crostata cool in the pan for at least 20 minutes before releasing. Dust with powdered sugar just before serving if you like.