Heat a large pot over medium-high heat. Add the olive oil, then the sausage. Cook, breaking the sausage into small pieces with a wooden spoon, until it is golden brown and no longer pink, about 6 minutes. With a slotted spoon, remove the sausage to a plate and set aside.
Reduce the heat to medium and add the garlic cloves. Cook for 1 minute.
Add the pasta, broth, 2 cups of water, oregano, salt, and pepper to the pot and bring to a simmer. Reduce heat to medium or medium low to keep it simmering for 5 minutes, stirring occasionally to prevent sticking.
Stir in the broccoli. Cover the pot and let cook until the pasta and broccoli are just tender, about 5 minutes, stirring half-way through.
Uncover the pot. Add the sun-dried tomatoes, heavy cream, and reserved sausage. Cook until heated through, about 1 minute.
Remove from the heat and stir in the parmesan cheese and lemon juice. Serve topped with more parmesan cheese and red chili flakes, if you like.