Combine pretzel twists and 1/4 cup brown sugar in a food processor; process until finely chopped. Stir in 1/2 cup melted butter. Press mixture over the bottom and sides of an ungreased 9-inch pie plate.
Combine 3/4 cup butter and chocolate chips in a microwave-safe bowl. Heat in the microwave, stirring once, until melted, 1 to 2 minutes. Stir in 3/4 cup brown sugar and white sugar until dissolved. Beat in eggs. Stir in heavy cream, flour, and vanilla extract until filling is smooth. Pour over the crust in the pie plate.
Bake in the preheated oven until center puffs up and looks set, about 50 minutes. Let cool completely, 1 to 2 hours. Drizzle caramel topping on top.