Remove the sausages from the casings. In a large skillet, heat 1 tbsp olive oil over high heat. Brown the sausage meat for 5 minutes, breaking it up with a spoon and stirring often.
In a pot, bring salted water to a boil. Add the broccoli and cook until very tender. Set aside in a bowl.
Using a potato masher, mash the broccoli until a puree is obtained.
In a large skillet, heat 1 tbsp of olive oil over medium heat and sauté the garlic and hot peppers for a few minutes, without letting them burn.
Stir in the broccoli mixture and sausage meat. Season with salt and pepper to adjust the seasoning if necessary. Add the pasta and mix.
Sprinkle generously with Parmesan and fresh basil.