Parmesan cheese, to garnish (if desired, omit for vegan)
Chop the onion. Mince the garlic. Chop the basil leaves.
In a medium pot, heat the olive oil over medium heat. Add the onion and sauté for about 4 to 5 minutes, until translucent. Add the garlic and red pepper flakes; sauté 1 minute until fragrant. Add the white wine vinegar and saute until evaporated.
Add the basil, canned tomatoes and their liquid, broth, kosher salt, and black pepper. Bring to a boil, then reduce heat and simmer 15 minutes. When done, remove from the heat and use an immersion blender to puree the soup until creamy.
Return to a simmer over medium heat. Add the gnocchi and cook for 3 to 4 minutes until they float, stirring occasionally so they don’t stick together or to the bottom.
Serve in bowls, allowing them to cool a few minutes until warm (soup tastes best warm, not pipping hot). Serve with chopped basil and Parmesan cheese (if desired; not required).