Set a large pot of water to boil. In a large skillet, cook sausage over medium heat, stirring and breaking up, until well browned, about 15 minutes. Transfer sausage to a paper towel. Add oil to skillet; return to medium heat. Cook onion and garlic with 1/4 teaspoon salt, stirring occasionally, until soft and golden, 2 to 3 minutes. Add grapes, broth and pepper flakes; increase heat to medium-high and cook, stirring occasionally, until grapes soften or burst and liquid thickens, about 10 minutes. Return sausage to skillet and stir; turn off heat. When water boils, add remaining 1 tablespoon salt and pasta; cook as directed on package. Drain pasta, add to skillet, and turn on heat to high. Cook, stirring, until sausage is hot and pasta is coated with sauce, 30 to 60 seconds. Divide pasta among 4 bowls; sprinkle each with Parmesan and parsley before serving.