Preheat your oven to 350°F (175°C). Place pretzels in a food processor and pulse until finely ground—aim for the consistency of coarse sand rather than powder. Transfer to a medium bowl.
Add granulated sugar and brown sugar to the crushed pretzels and mix well. Pour in melted butter and stir until the mixture resembles wet sand and holds together when pressed. Reserve about 3 tablespoons of the mixture for topping.
Press the pretzel mixture firmly into a 9-inch pie plate, starting with the sides and working toward the center. Use the bottom of a measuring cup to compact the crust evenly.
Bake the crust for 10 minutes, then remove and cool completely on a wire rack.
Increase the oven temperature to 375°F (190°C). Peel, core, and slice the apples into ¼-inch thick pieces.
In a large bowl, combine the sliced apples with sugar, flour, cinnamon, nutmeg, allspice, lemon juice, and vanilla extract. Toss gently until all slices are evenly coated. Let the mixture sit for 15 minutes.
Arrange the apple slices in the cooled pretzel crust, slightly mounding in the center. Pour any accumulated juices over the apples and dot with butter cubes. Sprinkle the reserved pretzel mixture around the edges.
Bake at 375°F for 45-50 minutes, or until the filling is bubbling and the apples are tender. If the crust edges start to darken too quickly, cover them loosely with aluminum foil.
Allow the pie to cool completely on a wire rack for at least 2 hours before serving to allow the filling to set properly.