Bring a large pot of salted water to a boil. Add the beans and cook until tender, about 2 minutes. Drain and dry well with paper towels.
Heat 2 tablespoons olive oil and the garlic in a medium saucepan over medium heat, stirring, until the garlic just starts browning, about 2 minutes. Stir in the tomatoes, basil, 1 teaspoon salt and 1/4 teaspoon pepper. Reduce the heat to low and bring to a low simmer. Cook, stirring, until the tomatoes start breaking down, 15 to 20 minutes.
Heat the remaining 1 tablespoon olive oil in a large skillet over medium-high heat. Add the beans and stir-fry until slightly browned and hot, 1 to 1 1/2 minutes; season with salt and pepper. Transfer to a platter and top with the tomatoes and ricotta salata. Season with more pepper.