Arrange two racks in the oven, one in the top third and the other in the bottom third. Heat oven to 425 degrees.

In a large bowl, toss squash with olive oil, honey and salt. Transfer to a large rimmed baking sheet. Roast, tossing occasionally, until golden brown at the edges and just tender, about 20 minutes. (They will cook more on top of the tart.)

Meanwhile, on a lightly floured surface, roll puff pastry into a 10-by-14-inch rectangle. Using a paring knife, lightly score a border along the perimeter of the puff pastry about a ¼ inch away from the edges. Place puff pastry on a parchment-lined baking sheet and, using a fork, prick the pastry inside the border to prevent puffing in the center.

Bake on the top oven rack until the puff pastry is very lightly golden at the edges (it won’t be baked through), 8 to 12 minutes. Transfer to a wire rack to cool slightly.

Brush tart crust all over with beaten egg and sprinkle with ¼ cup of the Parmesan, taking special care to coat the edges well with egg and cheese.

In a small bowl, stir together sour cream, remaining ½ cup Parmesan, thyme and black pepper. Spread on the puff pastry inside the border and arrange the squash decoratively on top. (If you don’t have room to use all the squash, snack on whatever is left.)

Bake until the squash is tender and the edges of the cheese mixture are golden brown, 18 to 22 minutes. Transfer to a rack to cool slightly (10 to 20 minutes) before serving.

Sprinkle with pistachios and flaky sea salt, drizzle with a little more hot honey and olive oil, and top with chives or parsley, and serve.