Using a large skillet, melt butter and olive oil on medium heat. Add mushrooms. Sauté until lightly browned. Add the shallots. Continue cooking until translucent. Sprinkle flour over mushrooms then slowly pour the Marsala wine over while stirring. Then pour in the chicken broth. The sauce will form as you stir in the ingredients together. Turn heat down to low and add the tuna.
Cook the linguine pasta according to the package directions. Usually about 7-9 minutes.
Drain the pasta and add directly into the pan with the sauce. Coat noodles evenly then plate, add parmesan cheese and garnish with parsley.