Preheat the oven to 400°F (204°C). Line two sheet pans with parchment paper and set aside for later.

Next, use a rolling pin to roll both sheets of puff pastry into 9×12-inch rectangles. Using a 2 1/4-inch cookie cutter (or another round object like a drinking glass or jar lid), cut as many circles as you can out of the puff pastry. Between both sheets, you should get about 32 circles.

Place the puff pastry circles on the prepared sheet pans 2-3 inches apart. (You may need to work in batches.) Use a smaller cookie cutter to score a circle in the center of each puff pastry circle. Don't cut all the way through. You just want to create a guide for the center of the tartlets.

Next, use the tines of a fork to dock the centers of the puff pastry circles. This will keep the pastry from puffing up too much. Then, whisk the egg with 1 Tablespoon (15 milliliters) of water. Use a pastry brush to brush the puff pastry circles with egg wash.

Bake the puff pastry circles for 5-6 minutes, just until they're starting to puff up. Remove the pans from the oven and use something small and circular to push down the centers of the tartlets. I either use a spoon or the lid of a bottle of vermouth (it's the perfect size!). Make sure to leave the borders nice and puffy. Then, bake the puff pastry circles for another 7-8 minutes, until they're golden-brown.

Remove the puff pastry circles from the oven and press down the centers if they've puffed up again. Then, fill the centers of each tartlet with 1 teaspoon of pepper jelly. Top each tartlet with a small slice of goat cheese. Bake the tartlets for 5 more minutes, just until the filling is warmed through.

Garnish the tartlets with fresh thyme. Serve immediately and enjoy!