Bring a large stockpot of cold water to a boil. Add rapini and blanch for 2 to 3 minutes.
Strain rapini and immediately cold water shock to stop the cooking process, by adding to an ice bath, or running freezing cold water over top.
Using the same water as you blanched the rapini, cook pasta until al dente (about 12-15 minutes). You can add 2 tbsp. of extra virgin olive oil to the water and 2-3 tbsp. of salt. Strain when finished cooking, but retain pasta water.
In the meantime, add 3 tbsp. of extra virgin olive oil to a large skillet over medium-high heat. Remove the sausage from the casing and crumble into the skillet. Brown the sausage, using a wooden spoon to stir and break into smaller pieces. When finished browning, transfer sausage from skillet into a plate or bowl and set aside.
Dry the rapini using paper towel and chop into bite-sized pieces.
Add butter to the skillet and brown (but don't burn) the butter. Add garlic and saute for a few minutes until the garlic is translucent and brown. Be careful not to burn the garlic.
Return the sausage to the skillet and add rapini. Saute for a couple of minutes.
Add 2 ladles of pasta water to the skillet to de-glaze. Add pasta and cheese, and saute in skillet to combine all the ingredients together.
Remove from heat and serve immediately. You can grate additional cheese over top before serving. Enjoy!