Heat the oven to 375°F. Line a rimmed baking sheet with parchment paper. Steam the chopped broccoli until just tender, about 3 to 4 minutes, then let it cool. Pat it dry so excess moisture does not loosen the filling.

In a large bowl, combine the ground turkey, egg, breadcrumbs, 1/4 cup milk, Dijon mustard, garlic powder, 1/2 teaspoon salt, and black pepper. Mix gently until combined, taking care not to pack the turkey mixture too firmly.

Turn the turkey mixture onto the prepared baking sheet and shape it into a rectangle about 1 inch thick. Sprinkle the broccoli and cheddar down the center, leaving a border around the edges. Fold the long sides over the filling and pinch the seams and ends closed. Turn the loaf seam-side down.

Stir the ketchup and Worcestershire sauce together in a small bowl. Brush the mixture over the top of the meatloaf. Bake until the center reaches 165°F, about 45 to 55 minutes. Let it rest for 10 minutes before slicing so the cheese has time to settle.

While the meatloaf bakes, place the potatoes and garlic cloves in a pot and cover with cold water. Bring to a boil, then reduce the heat and simmer until the potatoes are very tender, about 15 to 20 minutes. Drain well.

Return the potatoes and garlic to the pot. Add the butter, the remaining 1/4 teaspoon salt, and 1/3 cup milk. Mash until smooth, adding a little more milk only if needed to reach your preferred consistency. Serve the sliced meatloaf with the garlic mashed potatoes.