Heat the oven to 400°F. Line a 9-inch round cake pan with a circle of parchment paper.

Prepare the carrots: If your carrots are very thin (½ inch or less across at the top), cut them in half lengthwise. If they’re slightly thicker (more than ½ inch), quarter them lengthwise.

In a large sauté pan, heat the butter and honey together over medium-high heat until the butter is melted and the mixture is bubbly. Add the carrots, salt, pepper and thyme, and toss to coat. Cover with a lid, reduce the heat to medium and cook until the carrots are mostly cooked through, 12 to 15 minutes. Insert the tip of a knife into the thick end of a few carrots; you’re looking for a little tightness/resistance, but no crunch. While you’re cooking the carrots, occasionally lift the lid to stir and ensure they’re cooking evenly. If they’re browning in the pan, reduce the heat a little.

With the lid off, increase the heat, allowing most of the liquid to cook off. Add the vinegar, and cook, turning the carrots over in the sauce as carefully as you can without breaking them, until a small syrupy puddle remains, about 2 minutes more. Tip the carrots and all the pan juices into the prepared cake pan. Nudge them around so they evenly cover the bottom.

Assemble the tart: On a floured counter, roll out the puff pastry to a 10-inch round. Scatter goat cheese slices over the carrots in the pan. Top the carrots with the pastry, tuck in the dough edges all around and cut a vent in the center of the dough. Bake until the pastry is a deep golden brown, 25 to 30 minutes.

Remove the tart from the oven and let it rest for 10 minutes; then run a knife around the edges and flip it out onto a plate. Remove the parchment paper if it’s stuck to the carrots, and scrape any juices left in the pan over the tart. Nudge any wayward carrots back into place. Garnish the tart with additional thyme leaves and flaky salt. Cut into wedges with a serrated knife and serve.