In a large pot, add the olive oil and heat over medium heat. Add garlic and red pepper flakes; sauté about 1 minute, until just starting to brown. Add canned tomatoes and their liquid, vegetable broth, chopped basil, 1/2 teaspoon kosher salt and 1/4 teaspoon fresh ground black pepper. Bring to a boil. Reduce heat and simmer about 7 to 8 minutes.
Meanwhile, in a medium bowl, combine the ricotta cheese, the Parmesan cheese, eggs, flour, 1 teaspoon kosher salt, and 1/2 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 until solid, 5 to 10 minutes.
Thinly slice (chiffonade) a few extra basil leaves, and grate some Parmesan cheese. Serve the soup warm garnished with basil and Parmesan.