Browned Butter Apple Pie With Cheddar Crust

Place flours and salt in a food processor; pulse until blended. Add butter; pulse until butter is the size of peas. Add cheese; pulse 1-2 times. Transfer flour mixture to a large bowl. Gradually add ice water to flour mixture tossing with a fork until dough holds together when pressed. Divide dough in half. Shape each into a disk; wrap in plastic. Refrigerate 30 minutes or overnight.
Preheat oven to 400u0b0. For filling, in a Dutch oven, melt butter over medium heat. Heat 5-7 minutes or until golden brown, stirring constantly.
Stir in apples and sugars; bring to a boil. Reduce heat; simmer, covered, 6-8 minutes or until apples are almost tender. Uncover; cook 4-6 minutes longer or until slightly thickened, stirring occasionally. Stir in flour. Transfer apple mixture to a large bowl; refrigerate until cool.
On a lightly floured surface, roll out half of the dough to fit a 9-in. deep-dish pie plate. Transfer pastry to pie plate; trim pastry to 1/2 in. beyond edge of plate. Refrigerate 30 minutes.
Add filling to pastry. Roll remaining dough to a 12-in. circle; cut into eight wedges. Place wedges over filling. Trim, seal and flute edges. In a small bowl, whisk egg with water; brush over pastry.
Bake 45-55 minutes or until crust is golden brown and filling is bubbly. Cover edge loosely with foil during the last 15 minutes if needed to prevent overbrowning. Remove foil. Cool on a wire rack.