Place a large pot of water over high heat and bring up it up to a boil to cook the pasta, season with some salt and cook to al dente, according to package directions. Drain and reserve about 1 cup of the cooking water.
Heat 1 tablespoon extra-virgin olive oil in medium nonstick skillet. Add artichokes to heat through and lightly brown at edges.
To clean spinach, fill sink with water, swish spinach around and let grit fall to bottom of sink. Dry leaves before using.
In the bowl of a food processor add the shallot, 1/2 cup chicken stock, spinach leaves, mint, almonds and salt and pepper, to taste. If you have a hand held small-holed grater or a zester, grate garlic into the food processor. Adding a whole clove can result in stray big pieces of raw garlic, too bitter to bite down on. If you do not have a hand held grater, mince garlic and mash up into paste with a little salt. Turn processor on and add in about 2 tablespoons extra-virgin olive oil.
Scrape the spinach pesto into the artichoke pan and loosely cover with foil. Bring mixture to a simmer over low to medium-low heat and cook for about 2 minutes. Add the reserved pasta cooking water, the pasta and the cheese. Toss to coat the pasta with the sauce and heat for 1 minute. Transfer to a serving bowl or platter, season with salt and pepper, to taste, and serve.