Orecchiette with sausage and red grapes

6 oz. mild Italian sausage
1 tablespoon extra-virgin olive oil
1 small red onion, thinly sliced
2 cloves garlic, chopped
1 tbsp. salt
2 c. seedless red grapes
1 c. low-sodium chicken broth
1/4 tsp. red pepper flakes (or more to taste)
10 oz. whole-wheat orecchiette (small shells)
2 tbsp. grated Parmesan
1/4 cup chopped fresh parsley

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 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. Cook pasta. Drain, 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. Sprinkle with Parmesan and parsley before serving.