Combine garlic cloves, parsley, and Parmesan cheese in the bowl of a food processor fitted with the blade. Process until finely chopped. Add shallot and process until the mixture takes on a pesto-like appearance.
Scrape the mixture into a large bowl. Add egg, wine, and tomato paste, salt, and pepper and mix well to combine. Add meat and mix until the ingredients look evenly combined. Stir in about 1/2 cup of the breadcrumbs. If the mixture feels too soft and wet to shape, add remaining breadcrumbs until you achieve a firmer consistency that will hold its shape as it cooks.
Using a 2-tablespoon ice cream scoop, drop dollops of the mixture onto a rimmed baking sheet. Sprinkle with flour and, with well floured hands, roll into meatballs.
Heat olive oil in large, deep skillet over medium-high heat. Add meatballs and brown on the bottom. Turn gently and sprinkle with onion, shaking the pan to help the onion settle around the meatballs. Cook, turning the meatballs frequently, until they are browned on all sides and the onions have softened.
Add garlic and herbs to the skillet. Working carefully, add tomatoes and their juices, breaking them up with your fingers as you go. Pour in the wine and shake the pan to help the ingredients settle. Gently stir the mixture as best as you can without smashing the meatballs, which will be quite soft still. Bring to a simmer and reduce heat. Cook, partly covered, over low heat until the meatballs have cooked through and the sauce has thickened, about 30 to 40 minutes. Season with salt and pepper to taste.