Heat 3 tablespoons oil in a large saucepan over medium heat until shimmering. Add sliced garlic (5 cloves) and cook until lightly browned for about 1 minute. Stir in crushed tomatoes (1 28-ounce can), tomato sauce (1 15-ounce can), sugar (1/4 teaspoon), oregano (¼ teaspoon), salt (¼ teaspoon), Italian seasoning (2 teaspoons), and pepper flakes (¼ teaspoon). Bring to simmer; reduce heat to medium-low; and cook until slightly thickened, 10 to 15 minutes, stirring occasionally. Remove from heat and cover to keep warm.
Adjust oven rack to middle position and heat oven to 350°F. Place crackers (22) in a large zipper-lock bag, seal the bag and crush fine with a rolling pin (you should have about 1 cup of crumbs).
Combine crumbs, 2 cups Parmesan, egg (1), garlic powder (2 teaspoons), pepper (1 teaspoon), remaining 2 teaspoons oregano, and salt (¼ teaspoon) in a large bowl. Add chicken (2 pounds) and mix with your hands until thoroughly combined. Divide mixture into 20 portions (about ¼ cup each). Using your hands, roll each portion into a ball, and transfer to a 13 by 9-inch baking dish.
Pour sauce over meatballs, then sprinkle with mozzarella (8 ounces). Bake until meatballs register at least 160°F and mozzarella is melted and beginning to brown, 40 to 45 minutes. Let cool for 15 minutes.
Meanwhile, combine panko (1 cup), the remaining 2 tablespoons of oil, and remaining ¼ teaspoon salt, and 1 teaspoon Italian seasoning in a bowl. Microwave until panko is light golden brown, 1 to 3 minutes, stirring every 30 seconds.
Sprinkle meatballs with panko mixture, remaining ½ cup Parmesan, and basil (¼ cup). Serve.