Cook the noodles according to package directions.
Melt 3 tablespoons butter in a large saute pan. Add the garlic and cook 1 minute. Add the arugula and allow to wilt, about 1 minute. Add the lemon juice, salt and pepper and toss gently to combine well. Strain the pasta and add to the saute pan, tossing the noodles to combine. Add 1/2 the Asiago, toss and put in a serving bowl. Garnish with the remaining Asiago and a fresh crack of black pepper.