Preheat oven to 425°F. In the bowl of a stand mixer fitted with a paddle, add in the Cheddar cheese, mayonnaise, cream cheese, egg yolks, salt, pepper, mustard powder, Worcestershire sauce, hot sauce and thyme leaves. Stir together until well combined and set aside.
Heat the butter and 1 tablespoon olive oil in a large skillet over medium. Add the shallots, along with a pinch of salt and pepper, and cook, stirring occasionally, until they turn soft and begin to brown in spots, about 7 to 10 minutes. Remove them from the pan and set them aside.
Lightly flour a work surface and lay the puff pastry out flat. If your pastry comes in two pieces, lay them together to form a rectangle and crimp the edges together. Gently smooth out any creases with a rolling pin. Move the pastry to a baking tray lined with parchment paper. With a sharp knife, lightly score a 1-inch border around pastry. Use a fork to poke holes about an inch or so apart all over the middle part of the pastry, avoiding the border. Beat the whole egg in a small bowl and brush the border edges. Bake until light golden brown and slightly puffed, 10 to 15 minutes.
While the dough is par-baking, prep the apples. We like to leave the skins on though you can peel them if you like. Cut them in half, cut out the core with a melon baller or a paring knife, then slice them into very thin wedges using a mandoline or a sharp knife.
Remove the dough from the oven and spread the cheddar mixture over the pastry, staying within border. Scatter the reserved shallots over the top and arrange the apples over the top. Brush the apples lightly with the last tablespoons of olive oil and season them with salt and pepper, to taste. Return the tray to the oven and bake until the pastry is deep golden brown and the apples and shallots are caramelized, about 20 to 25 minutes. Let cool for at least 5 minutes before cutting and serving. Garnish with a little more fresh thyme, a sprinkle of spicy chili flakes and a drizzle of honey, if desired.