Heat the oven to 375°F and lightly grease a 9×13-inch baking dish. Position a rack in the center of the oven.
Make the sauce: Warm the olive oil in a large skillet over medium heat. Add the onion with a pinch of salt and cook until translucent and lightly golden, 5–6 minutes. Push the onion to one side, add the ground beef to the empty space, and cook, breaking it up, until browned with no pink remaining, 5–7 minutes; drain excess fat if needed.
Stir in the garlic and cook 30 seconds. Add tomato paste and cook until darkened slightly, about 1 minute. Pour in Worcestershire and Dijon, then add the tomato sauce and drained diced tomatoes. Season with smoked paprika, red pepper flakes, 1/2 teaspoon salt, and several grinds of pepper. Simmer gently, stirring occasionally, until the sauce thickens and tastes full, 10–12 minutes. Adjust seasoning to taste.
While the sauce simmers, boil the egg noodles in well-salted water until 1 minute shy of al dente according to package directions. Reserve about 1/2 cup pasta water, then drain (do not rinse).
In the empty pasta pot off the heat, combine sour cream, cottage cheese, and Parmesan. Add the hot noodles and toss until coated, loosening with a few tablespoons of the reserved pasta water as needed to make a glossy, creamy mixture.
Assemble: Fold about half of the beef sauce into the creamy noodles to marry the flavors. Spread the mixture in the prepared baking dish. Spoon the remaining sauce evenly over the top, then cover the surface with shredded cheddar.
Bake until bubbling at the edges and the cheese has melted, 18–22 minutes. For deeper color, switch to broil and brown the top for 1–2 minutes, watching closely.
Let the casserole rest 8–10 minutes to set. Scatter with chives, slice, and serve hot.