Preheat your oven to 350 degrees.
Spray a 9x13 glass or ceramic casserole dish with nonstick spray or butter your dish.
In a skillet over medium heat, add the olive oil.
Add the chopped onion, sprinkling with a bit of salt, and cooking until translucent.
Add the broccoli, cooking until fork tender.
Push the vegetables to the sides of the skillet and add the butter to the middle.
Once the butter is melted, add the flour into the butter and begin whisking, making sure to leave the vegetables to the sides. Whisk and cook the roux until it is glossy and light brown.
Add the dried herbs to the roux. Add black pepper to taste, then whisk in the milk by pouring it slowly into the roux, whisking the entire time. Try to stay in the middle, but it is okay if some of the vegetables start creeping into the mix.
Add in 2 cups of the shredded cheese, handful by handful, whisking after each one until the cheese is melted and incorporated.
Once the cheese is completely incorporated, whisk all the vegetables and sauce together to combine. Remove from the heat.
Add your rice to the skillet, stirring well to combine.
Pour the mixture into the casserole dish, packing the rice down into the dish. You want the mixture to be pressed into the dish, not loosely piled.
Top the casserole with the remaining shredded cheese.
Cover the dish with aluminum foil. You might spray the inside of the foil with a bit of nonstick spray if you're worried the cheese will stick to it.
Bake, covered, for 35 minutes at 350 degrees.
Remove the tin foil and continue to bake for another 10-15 minutes until the cheese is browned, bubbly, and delicious.