Preheat the oven to 425 degrees F (220 degrees C). Spray a 12-cup muffin tin with nonstick cooking spray.
Roll pie dough out onto a flat, clean surface. Cut round circles of dough that are wider than the muffin tin width. Press a dough circle into each of the prepared muffin cups. Cut round circles of aluminum foil and press over the dough circles; fill each with 1 tablespoon rice.
Place tart shells in the preheated oven. Decrease oven temperature to 400 degrees F (200 degrees C). Bake until set and golden, about 10 minutes.
While shells are baking, pour heavy cream, sugar, and vanilla extract into a large bowl. Beat using an electric mixer with a wire whisk attachment on medium speed until bubbly and frothy. Continue to beat until mixture starts to thicken and lines can be seen from the whisk, 2 to 3 minutes.
Increase mixer speed to medium-high until cream is billowy and doesn’t droop when whisk is turned upside down, 30 seconds to 1 minute. Beat for an additional 20 seconds if not ready, making sure not to over mix or it will be curdled. Place whipped cream in the refrigerator until tart shells are ready.
Remove tart shells from the oven. Let cool completely, 15 to 25 minutes.
Scoop even amounts of whipped cream into each tart shell. Top with peaches. Let chill in the refrigerator for 5 to 10 minutes.