Apple Pie with Cheese, Please Recipe

Ingredients

• 1 (9 inch) frozen pie crust, thawed
• 6 slices Cheddar cheese
• 5 medium apples - peeled, cored, and thinly sliced
• 0.5 cup butter
• 3 tablespoons all-purpose flour
• 0.5 cup white sugar
• 0.5 cup brown sugar
• 0.25 cup water
• 1 (9 inch) prepared pie crust, at room temperature
• 1 egg white
• 1 teaspoon water