Combine parsley, mint, yogurt, garlic, paprika, fennel seeds, 1 ½ teaspoons kosher salt, and red pepper flakes in a large bowl.
Add ground lamb and beef, and mix, using your hands, until combined. Form mixture into 1 ½ inch meatballs (about 2 ½ tablespoons each or #24 scoop (1.5 ounces)); transfer to a plate.
Heat oil in a large Dutch oven or braiser over medium. Arrange a few meatballs in an even layer in pot and cook until browned all over, about 5–8 minutes (depending on how hot your stove runs, you may need to lower the heat to avoid splattering). Transfer browned meatballs back to plate and repeat, in batches, with remaining meatballs.
Drain all but 2 tablespoons drippings from pot. Add shallots to pot; season with salt and cook until starting to soften, about 3 minutes.
Add tomatoes and cook, stirring occasionally, until some start to burst (you can help the tomatoes along by smashing them against the sides of the pan with a spoon), about 5 minutes.
Deglaze pan with vinegar, scraping up any browned bits. Stir in 1 ½ cups water, and bring to a simmer over high heat. Cook until sauce has slightly thickened but is still loose, 7–8 minutes.
Add meatballs and any accumulated juices to sauce, reduce heat to medium-low, and simmer until cooked through, about 8 minutes.
Sprinkle mint and pecorino over meatballs. Serve with warm crusty bread.