Core Roma tomatoes and coarsely chop. Put 2/3 of the chopped tomatoes into a food processor or blender. Add dried tomatoes, chilies, and basil; whirl until coarsely puréed.
In a 10- to 12-inch frying pan over medium-high heat, stir oil, shallot, and garlic until shallot is limp, about 2 minutes. Add remaining chopped tomatoes, puréed tomato mixture, and sherry. Simmer sauce over low heat, stirring occasionally, to blend flavors, 15 to 20 minutes. Add a little water if mixture begins to stick.
Meanwhile, cook pasta in about 3 quarts boiling water until barely tender to bite, 8 to 10 minutes. Drain and put in a wide serving bowl.
While pasta cooks, add shrimp to tomato sauce and stir often until shrimp are opaque but moist-looking in the center (cut to test), 3 to 5 minutes.
Mix sauce with pasta; sprinkle with parsley. Add salt and pepper to taste.