Heat 1 teaspoon of olive oil in a large pot over medium-high heat.
Add sausage and saute until well browned and cooked through, breaking it up with your spoon or spatula as it cooks. (Meanwhile, you can prep the remaining ingredients.)
Remove cooked sausage to a bowl using a slotted spoon and cover to keep warm.
Reduce heat to medium and in the same pot, heat remaining 2 teaspoons olive oil. Add chopped onion and saute for 4-5 minutes, until slightly tender. Add garlic, broccoli, salt and pepper and saute for 2-3 more minutes. Add tomatoes (undrained), Italian Seasoning, chicken broth and pasta. Return sausage to the pot and stir to get everything combined.
Increase the heat to high and bring the mixture to a boil. Then reduce heat to medium-low, cover and cook, stirring occasionally to keep the pasta moving so it all gets some time in the liquid. Cook for 12 to 15 minutes or until the pasta is al dente and the broccoli is tender.
Remove from heat and let sit, covered, for a few minutes. Top with grated Parmesan cheese and serve hot.