Remove puff pastry from the freezer and thaw according to package instructions. It should be ready by the time you make and cool the apple filling.
Brown the butter: In a medium saucepan, melt 2 tablespoons butter over medium heat. Once it begins to foam (1-2 minutes), stir occasionally as the milk solids turn golden brown. Within a few minutes, you’ll notice a nutty, caramel-like aroma and the butter will deepen to an amber color (around 4-5 minutes)–this is your cue to pull it off the heat. Be careful not to overcook, as it can go from perfectly browned to burnt very quickly. Let cool slightly while you peel and dice the apples.
Make apple filling: Peel, core, and dice apples into ⅓" pieces, and add to pot with browned butter. Add in brown sugar, cornstarch, vanilla, cinnamon, thyme, and salt. Bring to a simmer over low heat, stirring occasionally, until apples are softened and mixture has thickened slightly (around 5 minutes). Remove from heat, add fresh lemon juice, and set aside to cool for at least 30 minutes.
Once apple filling is cooked, line two large baking sheets with parchment paper.
Unroll thawed puff pastry onto parchment-lined baking sheets and very lightly roll with a rolling pin to smooth out dough into a square shape.
Using a sharp knife, cut each pastry sheet into 4 equal-sized squares (you will have 8 total). Place 1-2 tablespoons of apple filling in center of each square.
In a small bowl, whisk together the egg and water to create an egg wash.
Use a pastry brush or spoon to brush egg wash along the ½" edge of each pastry square. Fold opposite pastry corners together to form a triangle.
Use a fork or your fingers to crimp the edges together by pressing down gently. Place prepared turnovers in the fridge to chill for at least 20 minutes (this prevents leaking and ensures a flaky pastry).
Preheat oven to 400 degrees F. Brush each turnover with egg wash, and use a fork to pierce the top of each pastry to allow steam to escape. Bake for 18-22 minutes, until pastry is golden brown. Allow to cool for at least 15 minutes to avoid burning your mouth.