In a large pot, add 1 tablespoon olive oil and heat over medium heat. Add garlic and one pinch red pepper flakes; sauté about 1 minute, until just starting to brown. Add canned tomatoes and their liquid, 3 cups vegetable broth, chopped basil, ½ teaspoon kosher salt and ¼ teaspoon fresh ground black pepper. Bring to a boil. Reduce heat and simmer about 7 to 8 minutes.
Meanwhile, in a medium bowl, combine 1 cup ricotta cheese, 1 cup Parmesan cheese, 2 eggs, 1 ⅓ cup flour, 1 teaspoon kosher salt, and ½ teaspoon fresh ground pepper. Stir until a dough forms. Roll the dumplings into small balls (about 48). After the soup has simmered, place the dumplings in the soup and cook about 2 minutes until cooked through.
Thinly slice (chiffonade) a few extra basil leaves, and grate some Parmesan cheese. Serve the soup warm garnished with basil and Parmesan.