1 sheet of puff pastry (about 8 ounces), thawed slightly
1 large egg, beaten with a splash of water
1 cup of butternut squash ribbons, shaved with a vegetable peeler from the neck of the squash
Flaky sea salt
Freshly ground black pepper
1 tablespoon butter
1 medium shallot, thinly sliced
1/4 cup shaved Pecorino Romano cheese
Preheat oven to 375°F. Unroll the slightly thawed sheet of puff pastry onto a baking sheet and brush with a thin layer of the egg wash. Layer the squash ribbons over the puff pastry, leaving a 1-inch border.
Place a piece of parchment paper over the top of the tart. Place a second baking sheet on top of the parchment as a weight and bake for 10 minutes — this helps steam the butternut squash.
Remove the top baking sheet and parchment paper. Brush the squash with a thin layer of olive oil and season with flaky sea salt and freshly cracked black pepper. Bake for about 20 minutes, or until the dough is flaky and golden.
While the tart is baking, melt the butter in a small skillet over medium heat. Once the butter is hot, add the shallot slices and sauté until the slices crisp up and turn deeply golden-brown, 3 to 5 minutes. Transfer the crispy shallots to a paper towel and reserve until you are ready to serve.
When the tart comes out of the oven, sprinkle with the shaved Pecorino Romano cheese and the fried shallots. Cut into squares and serve.