Prepare the mixture by finely mincing the garlic and whisking the egg in a large mixing bowl. Add in the ground turkey, za'atar, bread crumbs, salt, and pepper. Mix thoroughly until all ingredients are well combined and the mixture is slightly sticky.
Using your hands, shape the mixture into 12-15 evenly sized meatballs, about 1.5 inches in diameter, and place them on a baking sheet or plate.
Heat a tablespoon of olive oil in a large skillet over medium heat. Once hot, carefully place the meatballs into the pan, spacing them apart. Cook for about 6-8 minutes, turning occasionally, until they are golden brown all over and have an internal temperature of 165°F (74°C).
If baking instead of pan-frying, preheat the oven to 400°F (200°C). Arrange the shaped meatballs on a lined baking sheet, brush lightly with olive oil, and bake for 15-20 minutes until cooked through and browned on the outside.
Once cooked, transfer the meatballs to a serving plate. Optionally, garnish with fresh herbs or a drizzle of lemon juice to enhance the flavors.