In a large bowl, mix the ground beef, egg, finely chopped onion, grated carrot, grated zucchini, grated sweet potato, minced garlic, breadcrumbs, salt, black pepper, sweet paprika, oregano, thyme, and parsley. Knead the mixture well and shape into meatballs.
Heat a little olive oil in a large pot or pan. Sear the meatballs on all sides for about 10 minutes until browned, then remove them from the pot and set aside.
In the same pot, add the tomato sauce, a pinch of salt, parsley, basil, sweet paprika, sugar, and most of the broth. Mix the flour with the remaining cold broth until smooth, then whisk it into the sauce. Simmer the sauce for 10-15 minutes to combine the flavors.
Return the meatballs to the sauce, cover with a lid, and cook on low to medium heat for another 35-45 minutes. Add a splash more broth or water if the sauce gets too thick.
Serve warm with a side of mashed potatoes, pasta, or rice.
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