Bring a large pot of water to a boil over high heat; cook spaghetti according to package directions. During the last 2 minutes of cooking, stir in spinach. Drain, reserving 1 cup cooking water.
Meanwhile, heat oil in a large skillet over medium-high heat. Add tomatoes, salt and pepper; cook, stirring occasionally, until the tomatoes start to soften and burst, about 6 minutes. Transfer ½ cup tomatoes to a small bowl. Stir basil into the tomatoes in the pan. Reduce heat to medium and cook, stirring often, until the tomatoes break down and become saucy, about 5 minutes.
Transfer the tomato mixture to a blender. Add 1 cup feta and ½ cup of the reserved cooking water. Secure the lid on the blender and remove the center piece to allow steam to escape. Place a clean towel over the opening; process until smooth and creamy, about 1 minute.
Return the sauce to the skillet; heat over medium heat. Add the drained pasta and spinach mixture and the reserved ½ cup tomatoes; toss to coat, adding more reserved cooking water as needed to reach desired consistency. Sprinkle with the remaining ½ cup feta; garnish with basil leaves, if desired. Additional reporting by Carrie Myers, M.S. and Linda Frahm
