Preheat oven to 350 degrees F (175 degrees C). Grease and lightly flour a 9-inch springform pan.
Combine flour, butter, and 2 eggs in a food processor; pulse several times until a soft pastry dough ball is formed and easily separates from the bowl; wrap tightly in plastic wrap and refrigerate for 15 minutes.
Grab pieces of dough, flatten with your hands, and cover the base and sides of springform pan. Spread a thin layer of dulce de leche over the pastry base.
Mix sugar, coconut, 2 eggs, vanilla extract, and coconut extract together in a bowl using a wooden spoon or your hands until mixture resembles breadcrumbs. Distribute mixture evenly over dulce de leche layer.
Bake in the preheated oven until golden, about 30 minutes. Cool pie to room temperature before removing the springform.