How to Make It
Wipe the herbs and spinach clean with a dry towel; if they are not organic, wipe them with a lightly dampened towel.
Put the sea salt in a large mortar. Add a few basil leaves, torn into fragments, and 1 garlic clove. Start grinding with the pestle in a circular motion until everything is reduced to a fine texture. Add a few more basil leaves and the spinach and grind and gently pound to the same fine consistency. Continue pounding the basil and herbs, adding the second garlic clove halfway through, until all the leaves are ground to a fine-textured pesto; keep scraping the pesto down into the bottom of the mortar as you work.
With the pestle, gradually stir in the 1/3 cup Parmesan and 3 tablespoons Pecorino cheese; you will have a very dense mixture. Scrape the pesto off the pestle and down from the sides of the mortar. Add the olive oil in a thin steady stream, stirring it in with the pestle in a circular motion until fully incorporated. One-half cup of olive oil makes a very loose pesto; you may want to use less for a thicker pesto.
Cook the spaghetti in a large pot of boiling salted water until al dente. Drain the pasta, reserving 1/4 cup of the cooking water. Transfer the pasta to a large bowl and toss with the pesto and 2 tablespoons of the pasta cooking water; add more water if necessary. Serve immediately, passing additional cheese at the table.