Preheat the oven to 425°. In a large bowl, using your hands, combine the beef, breadcrumbs, egg, garlic, salt, basil, oregano, cinnamon, pepper, parsley, rosemary, and cumin. Form into 1-inch balls and place on a rimmed baking sheet. Cook for 15 minutes, turning halfway through.
Meanwhile, in a medium bowl, stir together the yogurt, cucumbers, lemon juice, salt, pepper, dill, and garlic; set aside.
Remove the meatballs from the oven, let rest for 3 minutes before serving. To serve, add tzatziki sauce to a pita, place 3-4 meatballs on the sauce, and roll closed.