Bring a large pot of salted water to a boil. Boil pasta until al dente. Drain, reserving 1 cup of pasta cooking water.
While pasta boils, remove sausage from casing. In a large frying pan over medium heat, saute the sausage. Break up the sausage with a wooden spoon as it cooks.
When sausage has started to brown, about 5 minutes, add apple slices. Cook for 5 more minutes, stirring occasionally.
Add the cooked noodles, blue cheese, and 1/2 cup pasta cooking water to the sausage. Stir, breaking up the blue cheese and allowing it to melt. Add 1/4 to 1/2 cup more pasta cooking water if needed to loosen the sauce.
Add the arugula. Stir over medium heat until arugula has just wilted.
Serve hot!