01 - Preheat oven to 400°F. Lightly grease a 2-quart baking dish.
02 - Bring a large pot of salted water to a boil. Add cauliflower and broccoli florets and cook for 3 to 4 minutes until just tender. Drain thoroughly and set aside.
03 - In a medium saucepan over medium heat, melt butter. Whisk in flour and cook, stirring constantly, for 1 minute.
04 - Gradually pour in milk while whisking until smooth and slightly thickened, about 3 to 4 minutes. Remove from heat and stir in cheddar, Gruyère, Dijon mustard, nutmeg, salt, and pepper until cheeses are fully melted.
05 - Place drained cauliflower and broccoli evenly in the prepared baking dish. Pour cheese sauce over the vegetables.
06 - Combine Parmesan, breadcrumbs, and olive oil in a small bowl. Evenly sprinkle this mixture over the gratin.
07 - Bake for 25 to 30 minutes until the topping is golden and the gratin is bubbling.
08 - Allow the gratin to rest for 5 minutes before serving.