Place flour and 1/2 teaspoon salt in a food processor and pulse to combine. Add butter and cheddar cheese and pulse 4-5 times until pea-size chunks form in the flour. Pulse the ice water into dough until dough holds together when squeezed. If dough seems dry, add more water, a tablespoon at a time, until the dough just holds together.
Turn dough out onto a lightly floured work surface and bring together into a ball. Divide dough in half, cover each half tightly with plastic wrap and flatten into a 1-inch thick rounds. Refrigerate for 30 minutes or until dough is well chilled.
To Make the Filling:
Preheat oven to 375 degrees F. In a large bowl, combine apples, lemon zest and juice, sugar, cornstarch, cinnamon and pinch salt. Set aside while you roll out dough.
On a lightly floured surface, roll one dough into a round that fits into a 9-inch pie pan with enough for a 1-inch overhang. Transfer dough to pie plate and and use your hands to press into the dish. Spoon the apple filling into the dish, spreading evenly. Dot with 2 tablespoons cubed butter.
Roll the remaining pie dough out to a 1/4-inch thick round. Use a fluted pastry wheel to cut 12 1-inch wide strips. Arrange the dough in a lattice over the pie. Trim the edges to make a 1-inch overhang around the pie. Tuck dough under and crimp edges.
Whisk to combine egg yolk and heavy cream. Brush over dough and sprinkle with turbinado sugar. Place pie on a baking sheet and bake until center is bubbling and crust is golden, about 75-90 minutes. Let cool on a wire rack, slice to serve.