Preheat your oven to 375°F (190°C) and lightly grease a 9x13-inch baking dish with non-stick cooking spray. Set the dish aside.

Heat the olive oil in a large skillet over medium heat. Add the chopped onion and sauté for 4 to 5 minutes until softened and translucent, then add the minced garlic and cook for an additional 30 seconds until fragrant.

In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1 to 2 minutes until it forms a light golden paste, stirring constantly to prevent burning.

Gradually pour the vegetable broth and whole milk into the saucepan, whisking continuously to avoid lumps. Simmer the mixture for 3 to 5 minutes until it thickens enough to gently coat the back of a spoon.

Remove the saucepan from the heat and stir in 1.5 cups of the shredded cheddar cheese, dried thyme, salt, and black pepper. Stir continuously until the cheese is completely melted and the sauce is perfectly smooth.

In a large mixing bowl, combine the cooked brown rice, raw broccoli florets, and the sautéed onion and garlic mixture. Pour the warm cheese sauce over the top and gently fold everything together until all ingredients are evenly coated.

Transfer the mixture to the prepared baking dish, spreading it into an even layer with a spatula. Sprinkle the remaining 1/2 cup of cheddar cheese and the panko breadcrumbs evenly over the top.

Bake uncovered on the center rack for 25 to 30 minutes, or until the broccoli is tender, the edges are bubbly, and the breadcrumb topping is golden brown. Let the casserole rest for 5 to 10 minutes before serving to allow the creamy sauce to set.