Cover 1 9-inch unbaked pie shell with plastic wrap and refrigerate for 40 minutes, then freeze for 20 minutes.
Adjust oven racks to upper middle and lower middle positions and preheat to 375 degrees.
Line chilled pie shell with foil and top with pie weights.
Place 2 lbs ripe peaches cut side up on foil-lined baking sheet and sprinkle with 2 tbsp sugar. Bake on the upper middle rack until softened and juice starts to release, about 30 minutes, flipping halfway through baking.
Add pie crust to oven on the lower middle rack and bake for 15 minutes. Carefully remove foil and weights and bake crust and peaches for 5 minutes more. Remove and cool both crust and peaches for 15 minutes.
Reduce oven to 325 degrees. Cut peaches length-wise in quarters and arrange in a single layer over crust. Combine remaining 1/2 cup sugar, 3 tbsp flour, and 1/4 tsp salt in a large bowl.
Whisk in 1/3 cup heavy cream, 2 egg yolks and 1/2 tsp vanilla extract until smooth and pour the mixture over the peaches.
Bake until filling is light golden and set, about 45-55 minutes.
Cool for 3 hours before serving.
