Step 1Heat oven to 375 degrees. Roll out the pastry crust and place it in a 9-inch pie plate, creating a decorative edge for the border. Line the crust with aluminum foil and fill it with rice, beans or pie weights. Bake for 10 minutes, then remove the rice and foil, prick the bottom of the crust to prevent bubbling and return to the oven to bake another 10 minutes, until the surface is dry and set.
Step 2While the crust is baking, grind the almonds and sugar in a food processor until fine. Add the eggs, almond extract, vanilla extract and salt and process to make a thick, wet paste. With the processor running, pour 2 tablespoons of the melted butter through the feed tube.
Step 3Spread the almond paste across the bottom of the warm pie crust. It should be moist enough to spread evenly. Press the peaches into the almond paste, cut-side down, in a ring around the outside with one peach half in the center. Brush the remaining 1 tablespoon of melted butter on the peaches, then sprinkle lightly with sugar.
Step 4Bake on a cookie sheet in the bottom third of the oven until the peaches are glazed and the almond paste is puffed and brown and slightly crisp on top, about 50 to 55 minutes.