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1
Preheat the oven to 400u00b0 F. Have ready a 12-inch oven-safe skillet, preferably cast iron.
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2
Place the skillet over medium heat, melt the butter. Add the onions, rounded halves downward in the skillet. Arrange the onions as tightly as possible to fill the whole pan (remember, they will shrink as they cook). Cook, undisturbed, until the onions have softened slightly and begun to brown, 12-15 minutes.
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3
Gently flip the onions and season with salt and pepper, flip again so the browned side is down. Add the sherry and balsamic vinegar and bring to a simmer. Cook until reduced slightly 1-2 minutes. Add the herb sprigs in between the onions.
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4
Transfer the skillet to the oven and roast until the onions are golden and tender, 15-20 minutes more.
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5
While the onions cook, roll out the puff pastry on a lightly floured surface to flatten. Cut a circle about the size of the base of the skillet (totally ok to freehand here, no need to be perfect). Dock a few times with a fork.
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6
Remove the skillet from the oven, and use a fork or pair of tongs to push the onions together slightly-this should be easier now that they've softened. Gently drape the pastry over the onions, folding in a little at the edges to encase the onions.
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7
Return the pan to the oven and bake until the pastry is very golden brown, 20-25 minutes. Remove from the oven and cool for 5 minutes.
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8
Invert the skillet onto a cutting board to unmold the tarte tatin. Let cool for 5 minutes more. If using, serve with a generous grating of parmesan cheese.
