Heat the oven to 375°F with a rack in the middle position. Line a rimmed baking sheet with kitchen parchment, then mist the parchment with cooking spray. Cut each onion round in half crosswise and, using a wide metal spatula, transfer each round to the baking sheet, keeping the halves intact and spacing them evenly. Using your hands, slide the halves of each round in opposite directions so they are offset by about ½ inch. Drizzle each onion with about ½ teaspoon oil and sprinkle with salt and black pepper.

Lightly flour the counter and unfold the thawed puff pastry onto it. Using a rolling pin, roll the sheet into a 10- to 11-inch square. With a chef’s knife, cut the pastry in half; then cut each half crosswise into thirds, for a total of 6 rectangles. Using a fork, poke holes all over each.

Lay 1 puff pastry rectangle over each onion, pricked side facing up. Gently press the pastry to remove any air pockets between it and the onion. Using the fork, poke additional holes at the edges of each rectangle. Bake until the pastry is golden brown, about 20 minutes.

Meanwhile, unwrap the cheese, set it on a plate and place in the freezer. In a small microwave-safe bowl, stir together the honey and Aleppo pepper. Microwave on high just until warmed through, about 20 seconds. Set aside until needed.

When the tarts are golden brown, using a wide spatula, immediately invert them one at a time onto a serving platter or individual plates. Use a fork to reposition any onion slices that might have been dislodged. Working quickly, remove the cheese from the freezer, then cut thin slices and lay one over the onion on each tart. (The cheese will begin to melt as soon as it is placed on the tart; you may not use all of the cheese.)

Drizzle hot honey onto each tart, then sprinkle with 1 teaspoon thyme (if using) and additional black pepper. Serve warm.