Cook the pasta according to the instructions on the package. Save some of the pasta water for the end, if you desire a more saucy sauce.
Melt butter in a sauce pan.
Add the flour and stir until grainy and cooked through.
Peel and mince the garlic and add to the sauce pan, let cook for about a minute, make sure you don’t burn the garlic.
Add the milk and whisk vigorously to avoid lumps.
Add salt and pepper and let cook together. Be careful so it doesn’t boil over.
Cook until sauce has thickened, about five minutes.
Add the shredded cheese and keep stirring until the cheese is melted. If the sauce seems too thick, add some of the pasta water and stir again.
Add in the green pesto and stir.
Serve in a bowl over pasta and sprinkle more shredded cheese on top, if desire.