Heat the oven to 400°F. Lightly grease 8 cups of a standard muffin pan. Line a rimmed baking sheet with the broccoli florets.
In a large bowl, combine the ground turkey, egg, breadcrumbs, cheddar, onion, garlic powder, salt, black pepper, and ¼ cup of the BBQ sauce. Mix gently until just combined, taking care not to pack the mixture too firmly.
Divide the turkey mixture among the 8 prepared muffin cups. Shape each portion loosely so it fills the cup without pressing it down tightly. Brush the tops with the remaining ¼ cup BBQ sauce.
Toss the broccoli with the olive oil and spread it in an even layer on the baking sheet. Place the muffin pan and broccoli in the oven. Roast for 20 to 25 minutes, until the meatloaf muffins are cooked through and the broccoli is tender with browned edges. The turkey should reach 165°F in the center.
Let the muffins rest in the pan for a few minutes before removing them. Serve with the roasted broccoli.