Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Once water is boiling, stir in egg noodles and return to a boil. Cook pasta uncovered, stirring occasionally, until tender yet firm to the bite, about 5 minutes. Drain well in a colander set in the sink.

Preheat the oven to 350 degrees F (175 degrees C). Spray a 1-quart baking dish with nonstick cooking spray.

Mix together eggs and white sugar in a large bowl until thoroughly combined. Stir in melted butter, whipped cottage cheese, sour cream, salt, and pepper. Lightly mix in cooked noodles; spoon kugel into the prepared baking dish. Sprinkle the top with brown sugar.