Place a large pot of water on to boil. Add pasta and salt water. Cook to al dente.
While water comes to a boil, heat a deep skillet over medium heat. Add extra-virgin olive oil and butter. To warm oil and butter add crushed red pepper flakes, garlic and shallots, saute 3 minutes, add shiitake mushrooms and cook until tender, 3 to 4 minutes more. Deglaze the pan with sherry or Marsala wine, scatter in crabmeat - feeling for shell bits as you go. Warm the ingredients through, a minute or so, stir in tomatoes and heat through, 2 to 3 minutes. Stir in half-and-half or cream and reduce heat to lowest setting.
Drain pasta when cooked to al dente and toss with sauce and crab. Top with cheese, if using, and basil.