Step 1

Heat the oven to 350°F with a rack in the middle position. Coat a 9-by-13-inch baking dish with the 1 tablespoon room-temperature butter.

Step 2

In a 12-inch skillet over medium, melt the remaining 3 tablespoons butter. Add the leeks, mushrooms, parsley, thyme and ½ teaspoon salt. Cook, stirring occasionally, until the leeks and mushrooms are softened and lightly browned, 8 to 10 minutes. Remove the pan from the heat and let cool.

Step 3

Meanwhile, in a large pot, bring 4 quarts water to a boil. Add the noodles and 1 tablespoon salt, then cook, stirring occasionally, until just shy of al dente. Drain in a colander, then let cool until warm to the touch, about 10 minutes.

Step 4

While the noodles cool, in a large bowl, whisk together the eggs, sour cream, broth, goat cheese, ½ teaspoon salt and 1 teaspoon pepper until smooth; set aside. Add the leek-mushroom mixture and the noodles to the bowl with the egg mixture and stir. Pour the mixture into the prepared baking dish, distributing the noodles evenly.

Step 5

Bake until the kugel is golden brown on top, does not jiggle at the center when the dish is gently shaken and registers 160°F at the center, 40 to 45 minutes. Transfer to a wire rack and cool for about 10 minutes. Serve warm.