Prepare browned butter in a large skillet or shallow saucepan. Once browned, remove pan from heat, leave butter in pan and set aside.
Cook pasta according to al dente (pasta should be cooked, but still have a bite to it). Remove from heat and drain water from noodles but do not rinse them.
Add bacon onion relish to the pan with the browned butter. Put pan back onto medium heat. Cook, stirring occasionally, until relish is heated through.
Combine pasta to pan with sauce and stir to coat. Cook on medium heat for 1-2 minutes to warm thoroughly. Use pasta tongs to transfer pasta to serving plates. Garnish with freshly grated cheese and serve.