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Step 1
Preheat: Position oven racks in the upper- and lower-thirds of oven. Preheat to 425℉ (220℃).
Step 2
Roast Squash: Cut 1.5 lb acorn squash lengthwise, discard seeds, then slice into ¼-inch (0.6cm) half-moons. Spread squash on a large parchment-lined baking sheet. Toss with 1 tablespoon extra virgin olive oil. Sprinkle with 1 tablespoon fresh thyme leaves and ¼ teaspoon each fine sea salt and pepper and toss well. Bake on upper rack until golden-brown, 30 to 35 minutes, gently flipping halfway through. Let cool on a baking sheet.
Step 3
Bake Pastry: Meanwhile, unroll 1 sheet thawed puff pastry onto a lightly floured piece of parchment. Use a sharp knife to cut a ⅓-inch (0.8cm) wide strip from each side of the puff pastry (4 strips total). Prick the top of the large pastry sheet with a fork, then brush with 1 whisked egg (see note 7). Make a raised border by arranging the 4 strips of puff pastry on top of the outer edges of the puff pastry square. Brush top edges with more of the whisked egg (don't brush the sides). Slide the parchment with pastry onto a baking sheet. Bake on the lower rack until pastry is golden-brown and puffed up, 14 to 16 minutes. Let cool on baking sheet.
Step 4
Fry Sage: Meanwhile, warm 2 tablespoons extra virgin olive oil in a small pot over medium heat. Scatter in 10 fresh sage leaves and fry until crispy, 2 to 3 minutes. Transfer sage onto a plate lined with paper towel, and sprinkle with a bit of salt. (Keep oil in pot, removed from heat, and let cool).
Step 5
Whip Feta: Once the sage-infused olive oil has cooled, transfer to a food processor. To the oil, add ¾ cup crumbled feta cheese and 3 tablespoons plain Greek yogurt. Process until smooth, scraping down the sides as needed.
Step 6
Assemble: Once the puff pastry has cooled, top with the whipped feta. Shingle the cooled roasted acorn squash on top. Scatter with the fried sage (I like to crumble some and keep some whole). Drizzle with 2 tablespoons hot honey (adjust amount to taste), then sprinkle with 2 tablespoons chopped toasted pecans (if using). Season with more salt and pepper if needed. Cut into slices, then serve.