Bring a pot of water to a boil.
Preheat the oven to 350 degrees.
While the water is boiling heat a large sauté pan over medium heat.
Put in the olive oil and then the onion. Let the onion sauté for about five minutes or until it begins to soften.
Add in the sausage rounds and cook until they are cooked through, about 8-10 minutes.
Toss in the broccoli florets. I usually put the lid on for this last part to help the broccoli along. Cook an additional five minutes. The pan will be crowded. Remove to a large bowl and set aside.
Wipe out the inside of the sauté pan. Set it back over the heat.
Melt the butter.
While the butter is melting the water should be boiling for the pasta. Pour the pasta into the boiling water and set your timer according to package directions.
After the butter is melted, add in the flour and stir until the flour is combined with the butter and there are no lumps. About one minute.
Add in the chicken stock and allow it to come to a simmer. Stir occasionally and let it simmer until it is reduced and thickened. About ten minutes. Then pull it off the heat.
Toss in 1/2C of the grated Gruyere cheese. And stir until it is blended well. Stir in the salt and taste.
Drain the pasta into a colander and pour it into the bowl with the sausage and broccoli mixture.
Pour over the Gruyere gravy and stir. Pour everything into a 9"x13" casserole dish.
Top with the remaining shredded cheese.
Bake for 20 minutes or until bubbling and cheese has melted.