In a large pot of salted boiling water, cook the gnocchi for about 2 minutes or until they float to the surface of the water. Drain.
In a skillet over medium-high heat, melt the butter. Add the flour and continue cooking for 1 minute. Add the broth and bring to a boil, whisking constantly. Add the gnocchi and cheddar and stir gently until the cheese has melted completely. Season with salt and pepper. Set aside.
In a non-stick skillet over medium heat, brown the sausage meat in the oil, crumbling it with a wooden spoon. Add the tomatoes and green onion. Cook for 1 minute. Add the parsley. Season with salt and pepper.
Spread the sausage mixture over the gnocchi. Garnish with grated cheddar if desired.