Apple Noodle Kugel

3 large eggs
1/2 stick unsalted butter, melted and cooled
1/2 cup sugar, divided
1 teaspoon grated lemon zest
1/4 teaspoon grated nutmeg
1 1/2 pound Gala apples (about 3), peeled and coarsely grated on large holes of a box grater
5 ounces fine egg noodles (4 cups)

Accompaniment: sour cream

Preheat oven to 425 F with rack in upper third. Butter a 1 1/2-quart gratin or other shallow baking dish.

Whisk together eggs, butter, 7 tablespoons sugar, zest, and nutmeg in a large bowl until well combined, then stir in apples.

Cook noodles in a large pot of salted boiling water until al dente, about 5 minutes. Drain noodles, then toss well with apple mixture. Spread in baking dish and sprinkle with remaining tablespoon sugar.

Bake kugel until top is golden, about 30 minutes. Cool 5 minutes.