Bring salted water to a boil in a saucepan. Cook cauliflower until easily pierced with a fork, about 5 minutes. Transfer cauliflower to a baking dish with slotted spoon. Cook broccoli until easily pierced with a fork, about 2 minutes. Transfer broccoli to baking dish with slotted spoon.
Melt butter in a saucepan over medium heat. Add flour and whisk until beginning to brown, about 2 minutes. Whisk in milk and bring to a boil. Simmer, whisking constantly, until sauce is smooth and thickened, about 2 minutes more. Remove from heat; gradually whisk in 4 ounces Cheddar cheese. Stir in parsley, garlic, mustard, red pepper flakes, and nutmeg. Season with salt and pepper.
Pour sauce over cauliflower and broccoli; toss to coat. Combine tortilla chips and remaining Cheddar cheese in a small bowl; sprinkle over cauliflower and broccoli.
Bake in preheated oven for 10 minutes. Increase heat to broil; bake until bubbly and brown, about 5 minutes more.