Line two baking sheets with parchment paper or a silicone baking mat.
Roll out a sheet of puff pastry on each lined baking sheet.
Arrange apple slices overlapping but in a single layer in the center of the each puff pastry sheet, leaving ½ and inch of pastry exposed all the way around.
Top the apple slices with cheddar cheese, 2 ounces on each.
Drizzle 4 teaspoons of honey on top of apples and cheese and sprinkle ½ teaspoon of fresh thyme leaves on each galette.
Fold the ½ inch border of pastry inward to create a crust. Whisk egg and water together and brush over edges of puff pastry.
Bake in the oven for 400 Degrees F for 18-22 minutes or until pastry has browned and apple has softened slightly. Makes 2 galettes.