In a large pot, heat oil over medium-high. Add onion and garlic and cook until onion is translucent, about 6 minutes;season with salt and pepper. Add sausage and cook, breaking up meat with a wooden spoon, until browned, about 5 minutes
Add sweet potatoes, broth, and 2 cups water and bring to a boil. Add pasta and cook 3 minutes less than package instructions. reduce to a simmer, add greens, and cook until pasta is tender and greens are wilted, 4 minutes.
Serve with Parmesean