How to Make It
Preheat oven to 425°F. On a piece of lightly-floured parchment, roll one sheet puff pastry out to a 12-inch square; prick all over with a fork. Cut sheet into four 6-inch squares and fold in the edges of each square to create a ¼-inch border. Transfer parchment and pastry to a baking sheet. Repeat with second sheet.
In a small bowl, combine ricotta, chives, ½ teaspoon salt and several grinds pepper. Spread ricotta mixture onto each square. Arrange butternut squash over top, overlapping as necessary, and season with salt and pepper.
Bake until pastry is golden brown and squash still feels slightly firm, 15-18 minutes. Remove from oven.
Working with one egg at a time, crack eggs into a small bowl and gently slide into each of the puff pastry shells. Return to oven and bake until egg whites arejust set, 7 to 9 minutes. Serve topped with remaining chives and flaky salt.