Put oven rack in middle position and preheat oven to 400°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°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 purée in a food processor until smooth, about 45 seconds. Put 2 cups purée 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°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.

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Nutrition Facts

Per Serving Per 100 g

Amount Per 1 Serving
Calories	155.96 Kcal (653 kJ)
Calories from fat	97.78 Kcal
		% Daily Value*
Total Fat	10.86g	17%
Cholesterol	118.99mg	40%
Sodium	86.62mg	4%
Potassium	314.56mg	7%
Total Carbs	9.58g	3%
Sugars	1.14g	5%
Dietary Fiber	1.2g	5%
Protein	6.97g	14%
Vitamin C	12.6mg	21%
Vitamin A	0.6mg	19%
Iron	1.1mg	6%
Calcium	107.6mg	11%

Amount Per 100 g
Calories	106.55 Kcal (446 kJ)
Calories from fat	66.8 Kcal
		% Daily Value*
Total Fat	7.42g	17%
Cholesterol	81.29mg	40%
Sodium	59.18mg	4%
Potassium	214.91mg	7%
Total Carbs	6.54g	3%
Sugars	0.78g	5%
Dietary Fiber	0.82g	5%
Protein	4.76g	14%
Vitamin C	8.6mg	21%
Vitamin A	0.4mg	19%
Iron	0.8mg	6%
Calcium	73.5mg	11%

* Percent Daily Values are based on a 2000 calorie diet. Your daily values may be higher or lower depending on your calorie needs.
Find out how many calories should you eat.

Tastes

salty
savory
bitter
sweet

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