Place the grated garlic in a medium bowl along with the chives, parsley, yogurt, fennel seeds, paprika, salt, and crushed red pepper flakes. Mix until well combined.

Add the meat, season with pepper, and, using your hands, mix until well combined. Roll the mixture into balls about 1½ inches in diameter (about the size of a plum; I like these meatballs on the smaller side). Place on a baking sheet or large plate.

Heat the olive oil in a large, heavy-bottomed Dutch oven over medium-high heat. Add a few meatballs at a time, taking care not to crowd the pot. Cook, using tongs or a spatula to occasionally gently rotate them, until they are all golden brown all over (they may not hold their perfectly round shape, but that is more than okay), 8 to 10 minutes. As the meatballs are browned, transfer them to a large serving platter or plate. Leave the remaining bits and fat in the pot.

Add the shallot and sliced garlic to the pot and season with salt and pepper. Cook, stirring occasionally, until the shallot is tender and the garlic starts to brown a bit, 2 to 3 minutes.

Add the tomatoes and season with salt and pepper. Cook, stirring occasionally, until they burst and start to become all saucy and caramelize a bit on the bottom of the pot, 5 to 8 minutes. Add the vinegar and water, scraping up any bits along the bottom. Bring to a strong simmer and reduce the sauce by about one-fourth, just until it thickens slightly (it should still be relatively brothy), 5 to 7 minutes.

Return the meatballs to the pot and reduce the heat to medium-low. Simmer until the meatballs are cooked through and the flavors have melded, 10 to 15 minutes.

Remove from the heat. To serve, top the meatballs (either in individual bowls or right in the pot) with the mint and more crushed red pepper flakes and fennel seeds, if you like. Drizzle with some olive oil and serve with the cheese for grating and some toast for dipping.