To make crust: Sift flour, baking powder, and salt into a bowl and stir to mix. Set aside. With an electric mixer, beat together cream cheese and butter until well blended. Add vanilla and almond extract and stir to blend. Add sugar and stir until well blended. Add flour mixture, and blend thoroughly. Do not overmix.
With lightly floured hands, form dough into a flat round. Wrap and refrigerate until firm enough to handle, about 1 hour (dough will be slightly sticky).
On a lightly floured work surface, roll dough out into a 12-inch round, 1/4 to 1/2 inch thick. Roll dough up into bottom and sides of pan. Trim excess dough. Using a fork, press edges of dough down on lip of pie pan. Cover with plastic wrap and refrigerate 30 to 40 minutes or overnight before baking.
Preheat oven to 350 degrees, Bake crust until light brown and puffy, 25 to 30 minutes. Set aside to cool completely.
To make filling: In the meantime, peel, pit, and slice peaches. Mix with 1/2 cup sugar and spread evenly over prepared crust. Whip cream in a bowl with an electric mixer until soft peaks form; add remaining 1/4 cup sugar and beat until stiff. Top peaches with whipped cream and and refrigerate at least 2 hours but no longer than 8 hours.