Heat butter and olive oil over low heat in skillet; add garlic and cook just to soften and release flavor (do not brown) about 1 minute. Remove from heat and add tomatoes and basil. Allow sitting 30 minutes to blend flavors.
Cook pasta according to package directions; drain.
While pasta is cooking, heat the tomato mixture over low to medium heat; add crab and cook just to heat through, about 2-3 minutes then remove from heat. Add cooked pasta to tomato and crab mixture and toss to evenly mix; season with salt and pepper. Toss with Parmesan Cheese.
Recipe by A Year at the Table at https://ayearatthetable.com/angel-hair-pasta-with-dungeness-crab-tomatoes-and-basil/