Step 1: Begin by caramelizing the onions. Melt 2 tablespoons of butter in a large skillet over medium-low heat. Add the sliced onions and 1/2 teaspoon of salt. Cook, stirring occasionally, for 30-40 minutes, until deeply golden brown and soft. Remove from heat and set aside.
Step 2: While onions are caramelizing, prepare the brown butter. In a small, light-colored saucepan, melt the remaining 4 tablespoons of unsalted butter over medium heat. Continue to cook, stirring occasionally, until the butter foams, then turns golden brown with nutty aromas. Immediately remove from heat and pour into a heatproof bowl to stop cooking. Let it cool slightly.
Step 3: Cook the egg noodles. Bring a large pot of salted water to a boil. Add the wide egg noodles and cook according to package directions until al dente. Drain well and rinse with cold water to prevent sticking. Transfer to a large mixing bowl.
Step 4: Preheat your oven to 375°F (190°C). Grease a 9x13 inch baking dish with butter or cooking spray.
Step 5: In a separate large bowl, whisk together the eggs, sour cream, cottage cheese, milk, cooled brown butter, granulated sugar, remaining 1/2 teaspoon salt, and remaining 1/2 teaspoon black pepper until well combined.
Step 6: Add the cooked and drained noodles to the egg mixture. Gently fold in the caramelized onions until everything is evenly distributed.
Step 7: Pour the noodle mixture into the prepared baking dish, spreading it evenly.
Step 8: Bake for 45-55 minutes, or until the kugel is golden brown on top and set in the center. A knife inserted into the center should come out clean.
Step 9: Let the kugel rest for 10-15 minutes before serving. This allows it to set further and makes for cleaner slices.