Add the olive oil and sausage to the skillet and cook over medium heat until browned. If using links, cook them until browned on the outside and firm enough to slice, then slice into medallions, return to the skillet, and brown on both sides. Transfer the cooked sausage to a clean bowl and drain off all but about 1 Tbsp fat from the skillet.
Add the minced garlic and frozen broccoli florets to the skillet. Sauté over medium heat for 3-5 minutes, or just until the broccoli is bright green and no longer frozen. Transfer the broccoli florets to the bowl with the sausage.
Add the chicken broth to the skillet and stir or whisk to dissolve the browned bits off the bottom of the skillet. Slice the sun dried tomatoes into strips and add them to the broth with the pasta and a pinch of red pepper flakes. Stir, place a lid on top, and turn the heat up to medium high. When the broth begins to boil, give the skillet a quick stir, replace the lid, and turn the heat down to low or just above low so that the broth maintains a simmer.
Simmer the pasta and sun dried tomatoes for about 7 minutes, stirring every couple of minutes, or until the pasta is tender and most of the liquid is absorbed. If the pasta becomes tender before all the broth has been absorbed, simply let it simmer for the last couple of minutes without the lid.
Once the pasta is tender and only a small amount of thickened liquid remains in the bottom of the skillet, add the cooked sausage and broccoli back to the pasta. Stir to combine and sprinkle the grated Parmesan over top. Serve immediately.