Prepare the Pie Shell: Roll out one half of the double crust pie dough and gently press it into a 9-inch pie plate. Trim the edges and preheat your oven to 375°F (190°C).

Create the Apple Filling: Toss the sliced Honeycrisp apples with lemon juice. Add brown sugar, granulated sugar, flour, cinnamon, nutmeg, and salt. Stir until apples are well-coated, then blend in vanilla and heavy cream.

Cook the Filling: In a large pot over medium heat, melt the butter and add the apple mixture. Cook for 6-8 minutes, stirring frequently until apples soften slightly. Remove from heat.

Assemble the Pie: Pour the cooked apple filling into the prepared pie shell and spread it out evenly.

Make the Crumble Topping: In a mixing bowl, combine flour and granulated sugar. Cut in butter until coarse crumbs form. Stir in chopped chocolate-covered toffee bits.

Top the Pie: Sprinkle the crumble mixture over the apple filling. Roll out the second half of the pie dough, place it over the topping, and cut slits for steam.

Finish with Egg Wash: Beat the egg white with water and brush it over the top crust, then sprinkle with turbinado sugar.

Bake the Pie: Place the pie on a baking sheet and bake for 50-60 minutes, until the crust is golden brown and the apples are tender.

Cool and Slice: Let the pie cool slightly, then slice into it and serve your Toffee Crumble Apple Pie!