Bring a pot of water to a boil and add salt and the pasta. Cook until al dente. Reserve about 1/2 cup of the cooking water before draining the pasta, and don't wash the pot. (see Use pasta water to adjust a sauce's thickness)
As the pasta cooks, wilt the spinach and make the pesto in a mortar or blender as follows:
Put the wet spinach in a large skillet over medium heat. Add a dash of salt, cover, and cook for 3 to 4 minutes. Remove the pan from the heat, keeping the lid on; the spinach will wilt and stay bright green.
If using a blender, put in the garlic, anchovies, capers, lemon zest, the 2 Tbs. crumbled feta, the parsley, basil, lemon juice, olive oil, salt, and pepper and blend until the pesto is creamy. If using a mortar, add the pesto ingredients one at a time, pounding with a pestle until well mashed and blended before adding the next ingredient. Thin the pesto with the reserved pasta water to get the consistency of runny cream; you probably won't have to use the entire 1/2 cup water.
Return the pasta to the pot in which it was cooked; add the spinach (drain any liquid left in the pan) and the pesto, stirring very well to coat the pasta. Stir in the 2/3 cup crumbled feta and serve.