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Arrange a rack in the middle of the oven and heat to 400°F.
Heat the oil in an ovenproof 9- or 10-inch skillet, preferably cast iron, over medium heat until shimmering. Add the tomatoes and season lightly with salt and pepper. Cook, stirring once or twice, and as tomatoes begin to pop and release their juices, use a slotted spoon to press each down gently to release even more of their juice, then transfer them to a plate. All of the tomatoes should have popped after 8 to 10 minutes. Remove the pan from the heat (do not clean) and let the tomatoes cool on the the plate to the touch, 5 to 10 minutes.
Once the tomatoes are cool enough to handle, return the skillet to medium heat and add the vinegar and honey. Bring the mixture to a simmer and cook until reduced slightly, thick, and syrupy, about 1 minute.
Remove the skillet from the heat. Use your fingers to gently return the tomatoes to the skillet in one even layer, nestling them beside each other to fit as needed. Leave any juices that have collected on the plate behind. Sprinkle the chopped thyme over the tomatoes along with another big pinch of salt and a few grinds of black pepper.
Place the puff pastry round on top of the tomatoes, folding under any edges, if needed. Prick the pastry with a fork in a handful of spots.
Bake until the puff pastry is golden-brown, 25 to 30 minutes. Remove from the oven, let stand for 5 minutes, then run a knife around the pastry to loosen it from the pan. Invert a large plate over the top of the skillet and, using oven mitts, carefully and quickly flip the tarte tatin onto the plate. Rearrange any tomatoes that may have fallen out of place. Garnish with the thyme sprigs and serve warm or at room temperature, cut into wedges.