Preheat the oven to 400°F.
In a large pot, cook the rice with a pinch of salt according to package instructions.
On a large rimmed baking sheet, toss the broccoli with 1 tablespoon olive oil, ½ teaspoon salt, red pepper flakes, and garlic powder. Roast for 12-15 minutes, until lightly charred around the edges.
Meanwhile, in a small bowl, toss the breadcrumbs with the remaining 1 tablespoon olive oil, remaining ¼ teaspoon salt, and pepper.
Combine the cheeses in a separate small bowl.
Add the nutritional yeast, garlic, 1½ cups of the cheese, milk, and broccoli to the rice. Stir well.
Transfer the rice and broccoli mixture to a 9x9-inch baking dish. Top with the breadcrumbs and remaining ½ cup cheese.
Bake, uncovered, for 20-25 minutes, until the edges are golden. Cool for 5-10 minutes before serving.