Perfect Potato Hash

Name: Perfect Potato Hash
Ingredients: 1 1/2 pounds Yukon gold potatoes (about 3 large); 1 1/4 teaspoons kosher salt, divided, plus more as needed; 1 small yellow onion (about 6 ounces); 1 small red bell pepper (about 6 ounces); 4 cloves garlic; 1/2 small bunch fresh parsley; 1 ounce Parmesan cheese, finely grated (about 1/4 cup), plus more for serving; 2 tablespoons olive oil; 2 tablespoons unsalted butter; 1/4 teaspoon freshly ground black pepper, plus more as needed; 1/2 teaspoon sweet paprika