01 - Bring a large pot of salted water to a rolling boil. Add egg noodles and cook according to package directions. During the final 3 minutes of cooking, add the broccoli florets to the pot. Drain thoroughly through a colander and set aside.
02 - Set a large oven-safe skillet over medium heat and melt the butter. Add the chopped onion and sauté for 3–4 minutes until softened and translucent. Stir in the minced garlic and cook for an additional 1 minute until fragrant.
03 - Sprinkle the flour evenly over the softened onion mixture. Stir constantly for 1–2 minutes, allowing the roux to cook until it turns a light golden color.
04 - Gradually pour in the whole milk while whisking vigorously to prevent lumps from forming. Bring the mixture to a gentle simmer and continue cooking for 3–5 minutes, stirring occasionally, until the sauce coats the back of a spoon.
05 - Season the sauce with kosher salt, black pepper, paprika, and Dijon mustard if using. Reduce the heat to low, add the shredded sharp cheddar cheese, and stir continuously until completely melted and silky smooth.
06 - Add the drained noodles and broccoli to the skillet. Toss gently but thoroughly, ensuring every strand and floret is evenly coated in the creamy cheddar sauce.
07 - If desired, sprinkle grated Parmesan cheese and breadcrumbs evenly across the surface. Transfer the skillet under a preheated broiler for 2–3 minutes until the topping turns bubbly and golden brown.
08 - Serve immediately while hot, garnished with additional shredded cheddar or fresh herbs as desired.