Preheat the oven to 375°. In a Dutch oven, melt the butter over medium heat. Add the rice and scallions. Cook, stirring constantly, until the rice is toasted, 2 to 3 minutes.

Add the stock, milk, broccoli, and kosher salt and bring to a boil. Remove from heat.

Stir in the cheddar and mozzarella; season with pepper. Top with the Parmesan. Bake until golden, about 30 minutes.