Pour the tomatoes and their juice into to a blender and pulse to a very coarse puree. Heat the oil in a medium (3-quart) saucepan over medium. Add the garlic and chile and cook, stirring until the garlic softens and begins to brown, about 1 minute. Add the tomatoes to the saucepan, and cook, stirring nearly constantly, until the mixture has reduced to the consistency of tomato paste, about 7 minutes. Add the broth and simmer over medium-low until the sauce is the consistency of cream soup, 20 to 30 minutes. Taste and season with salt, usually a generous 1/2 teaspoon.