- 1 (2 1/2 pound) butternut squash, halved lengthwise and seeded
- 4 large eggs
- 2 egg yolks
- 2 cups half-and-half
- 1 1/8 ounces finely grated Parmigiano-Reggiano
- 4 large sage leaves
- 2 teaspoons finely chopped fresh sage
- Put oven rack in middle position and preheat oven to 400 degrees F.
- Roast squash, cut sides down, in a lightly oiled shallow baking pan until neck is tender, about 1 hour. Remove from oven and reduce oven temperature to 325 degrees F. Cool squash to warm.
- Butter an 8- by 2-inch round cake pan. Line bottom with a round of parchment or wax paper and butter paper.
- Scoop flesh from squash, discarding skin, and puree in a food processor until smooth, about 45 seconds. Put 2 cups puree in a bowl, then whisk in whole eggs, 1 cup half-and-half, 2 tablespoons cheese, 1 1/4 teaspoons salt, and 1/2 teaspoon black pepper until combined.
- Pour squash mixture into cake pan and bake in a water bath until just set and a wooden pick or skewer comes out almost clean, 45 minutes to 1 hour. Remove from water bath and cool flan in pan on a rack 15 minutes. Invert a flat plate over flan, then invert flan onto plate and carefully remove parchment.
- Meanwhile, bring whole sage leaves and remaining cup half-and-half just to a simmer in a 1- to 2-quart heavy saucepan, then remove from heat and let steep, covered, 10 minutes.
- Remove sage, carefully squeezing leaves to extract liquid, and discard leaves.
- Whisk yolks into half-and-half and cook over moderately low heat, stirring constantly with a wooden spoon, until sauce is thick enough to coat back of spoon and registers 170 to 175 degrees F on thermometer, about 4 minutes (do not let boil).
- Immediately pour sauce through a fine-mesh sieve into a bowl, then add remaining 1/2 cup cheese and chopped sage, stirring until cheese is melted. Stir in 1/4 teaspoon salt and 1/2 teaspoon pepper.
- Cut flan into wedges with a thin knife, wiping knife clean after each slice. Serve flan with sauce.