Heat the oven to 400°F. Line a 12-cup muffin pan with paper liners or lightly coat it with cooking spray.
Rinse the quinoa in a fine-mesh strainer. Combine it with the water in a small saucepan and bring to a boil. Cover, reduce the heat to low, and simmer until the water is absorbed and the quinoa is tender, about 15 minutes. Let it cool slightly.
Put the broccoli florets on a sheet pan and toss them with the olive oil, 1/4 teaspoon of the salt, and a pinch of the black pepper. Spread them in a single layer.
In a large bowl, combine the ground turkey, cooked quinoa, egg, onion, breadcrumbs, 2 tablespoons of ketchup, Worcestershire sauce, garlic powder, and the remaining salt and pepper. Mix gently until just combined.
Divide the turkey mixture among the muffin cups, filling each about three-quarters full. Brush the tops with the remaining 2 tablespoons of ketchup.
Place the muffin pan and broccoli pan in the oven. Roast the broccoli until browned at the edges and tender, about 20 to 25 minutes. Bake the meatloaf muffins until cooked through, about 20 to 25 minutes. The center of a muffin should reach 165°F. Remove each pan when its food is ready.
Let the muffins rest for a few minutes before serving them with the roasted broccoli.