01 - Preheat the oven to 375°F. Grease a 2-quart baking dish.
02 - In a large pot of salted boiling water, blanch broccoli, cauliflower, and carrots for 3 to 4 minutes until just tender. Drain and set aside.
03 - Melt unsalted butter in a saucepan over medium heat. Add diced onions and sauté for 3 minutes until softened. Stir in flour and cook for 1 minute to form a roux.
04 - Gradually whisk in whole milk, stirring constantly. Cook until the sauce thickens, approximately 3 to 4 minutes. Remove from heat and incorporate grated cheddar cheese, salt, black pepper, and ground nutmeg until smooth.
05 - Mix the blanched vegetables into the cheese sauce, then transfer the combined mixture into the prepared baking dish.
06 - In a small bowl, combine fresh breadcrumbs, grated Parmesan cheese, and olive oil. Sprinkle evenly over the vegetable and sauce mixture in the baking dish.
07 - Bake in the preheated oven for 25 to 30 minutes, or until the topping is golden brown and the mixture is bubbling.
08 - Allow the dish to rest for 5 minutes before serving.