Preheat the oven to 450˚ F. Combine the onion, chopped carrot and garlic in a food processor and pulse until finely chopped; transfer to a large bowl. Add the turkey, egg, panko, milk, 2 tablespoons hot sauce, 1/4 teaspoon salt and a few grinds of pepper. Mix well with your hands. Form into four 3/4-inch-thick oval patties on a rimmed baking sheet.
Bake the patties until lightly browned, firm and a thermometer inserted into the centers registers 160˚ F, 20 to 25 minutes.
Whisk the melted butter and remaining 1/3 cup hot sauce in a bowl. Brush the tops of the meatloaves with half of the sauce, then return to the oven until the sauce is baked in, about 4 minutes. Remove from the oven and brush with the remaining sauce.
Transfer the meatloaves to plates. Toss the broccoli, grated carrots and celery with the blue cheese dressing; serve with the meatloaves.