Bring a pot of salted water to a boil. Meanwhile, heat the olive oil in a large skillet over medium heat. Add the leeks, garlic and turkey and cook, stirring, until the turkey browns slightly, about 5 minutes. Add the tomatoes, 2 cups water and 1/4 teaspoon each salt and pepper. Increase the heat to high, bring the sauce to a boil and cook 5 minutes. Reduce the heat to medium, add half of the basil and the parmesan rind and simmer, stirring occasionally, until thickened, about 10 minutes.
Add the pasta to the boiling water and cook as the label directs. Reserve 1/2 cup of the cooking water, then drain the pasta. Stir the half-and-half, the remaining basil and 2 tablespoons cheese into the sauce. Add the pasta and toss to coat, adding some of the reserved pasta water to loosen, if needed. Remove the parmesan rind and season with salt and pepper.
Divide the pasta among bowls. Top with the remaining 1 tablespoon cheese and more basil.