Heat olive oil in a saucepan and cook garlic until lightly golden brown and fragrant, about 1 minute. Carefully add tomatoes, tomato paste, salt, and pepper; stir to combine. Simmer sauce, stirring occasionally, until thickened, about 20 minutes. Remove from heat and mix in basil. Stir to combine, taste, and adjust seasoning with salt and pepper. Set aside.
Season cube steaks with salt and pepper on both sides. Set 3 shallow dishes on the counter. Add flour and garlic salt to the first, beaten eggs to the second, and bread crumbs to the third. Season eggs with 1/2 teaspoon salt and 1/4 teaspoon pepper.
Coat each cube steak lightly with flour and tap off excess. Dip cube steak in beaten eggs, allowing excess egg to drip off before turning cube steak in bread crumbs. Press bread crumbs into the cube steak to make sure they adhere. Transfer breaded cube steak to a wire rack-lined baking sheet. Continue this process until all cube steaks are coated.
Heat oil in a large skillet over medium heat until shimmering. Place cube steak gently into the skillet and cook on the first side until golden brown, 2 to 3 minutes. Turn over carefully and cook on the second side until golden brown, 2 to 3 minutes longer. Return to the baking sheet to drain.
Set an oven rack about 8 to 10 inches from the heat source and preheat the oven's broiler. Line a rimmed baking sheet with parchment paper.
Transfer cube steaks to the lined baking sheet and place the sliced mozzarella cheese evenly on top. Broil until mozzarella has melted and begins to brown, about 5 minutes. Spoon the tomato sauce over each cube steak before serving.