01 - Bring a large pot of salted water to a rolling boil. Add the egg noodles and cook according to package directions. During the final 3 minutes of cooking, add the broccoli florets to the pot. Drain everything 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 cook for 3 to 4 minutes until softened and translucent. Stir in the minced garlic and cook for 1 additional minute until fragrant.
03 - Sprinkle the flour over the softened onions and garlic. Stir constantly for 1 to 2 minutes until the mixture turns a light golden color and loses its raw flour smell.
04 - Gradually pour in the whole milk while whisking vigorously to prevent lumps. Bring the mixture to a gentle simmer and continue cooking for 3 to 5 minutes, stirring occasionally, until the sauce thickens enough to coat the back of a spoon.
05 - Season with kosher salt, black pepper, paprika, and Dijon mustard if using. Reduce the heat to low, add the shredded cheddar cheese, and stir continuously until fully melted and silky smooth.
06 - Add the drained noodles and broccoli to the skillet. Toss gently with tongs or a large spoon until everything is evenly coated in the cheddar sauce.
07 - Sprinkle the grated Parmesan and breadcrumbs evenly over the top. Transfer the skillet to the oven and broil for 2 to 3 minutes until the surface is bubbly and golden brown. Watch carefully to avoid burning.
08 - Remove from the oven and let rest for 1 to 2 minutes. Serve hot, garnished with additional cheddar shreds or fresh herbs if desired.