In a large mixing bowl, combine all-purpose flour, sharp cheddar cheese, fresh thyme, and salt. Cut in cold unsalted butter until resembling coarse crumbs. Gradually add vodka until dough forms. Chill for 1 hour.

Preheat oven to 375°F (190°C). Wash and slice honeycrisp apples into thin rounds. Toss apple slices with sugar until well coated.

Roll chilled dough into a 12-inch circle on a floured surface. Transfer to a parchment-lined baking sheet and sprinkle cheddar in the center. Arrange apple slices on top of cheese.

Fold edges over filling, overlapping to create a rustic look. Chill assembled galette for 10-15 minutes.

Brush edges with egg wash or milk. Bake for 35-40 minutes until golden brown and bubbling.

Cool for 10-15 minutes before slicing. Drizzle with honey before serving.