Heat olive oil in a large pot or Dutch oven over medium heat. Add the minced garlic and diced onion, and sauté for 2-3 minutes until fragrant and softened.

Whisk in the flour and cook for 1 minute, stirring constantly to form a roux.

Gradually pour in the milk and vegetable broth, whisking continuously to prevent lumps. Stir in the Dijon mustard, smoked paprika, salt, and black pepper. Bring the sauce to a gentle simmer over medium heat, then reduce the heat to low.

Add the dry elbow macaroni and broccoli florets to the pot. Stir to combine. Cover the pot and cook for 12-15 minutes, stirring occasionally to prevent sticking. If the mixture seems too dry during cooking, add 2-3 tablespoons of water as needed.

Remove the pot from the heat. Stir in the shredded cheddar cheese and grated Parmesan cheese until fully melted and the sauce is silky smooth. Taste and adjust seasoning if needed. Serve immediately, topped with optional red pepper flakes or fresh parsley.