In a large pot of boiling, salted water, cook the pasta until al dente. Drain, reserving 1/4 cup cooking water, and return to the pot.
Meanwhile, in a medium skillet, heat the olive oil over medium heat. Add the garlic and cook until golden, about 4 minutes. Stir in the tomatoes, spinach and the reserved pasta water and cook until heated through, about 4 minutes. Season with salt and pepper. Stir into the pasta along with the goat cheese. Transfer to a serving dish and sprinkle the walnuts on top.