1. Heat oil in a large saucepan over medium heat until hot but not smoking. Add onion and garlic; cook, stirring occasionally, until onion is translucent, 5 to 7 minutes. Add wine; cook until most liquid has evaporated. Add tomatoes and juice, tomato sauce, basil, and red pepper flakes. Reduce heat to medium-low; simmer until slightly thick, about 30 minutes. Season with salt and pepper. Remove from heat; cover to keep warm.

2. Bring a large pot water to a boil; add 1 tablespoon salt. Add half of the gnocchi; when they rise to the top (after about 2 minutes), continue to cook until tender, about 15 seconds more. Transfer gnocchi with a slotted spoon to pan with sauce. Repeat process with remaining gnocchi.

3. Reheat gnocchi over low heat; gently toss. Serve with cheese shavings.