Place a large pot of water over high heat and bring to a boil for the pasta.
Trim off the root ends and top four inches of the leeks. Cut them in half lengthwise then into slices 1/4-inch thick. Wash them vigorously, separating the layers to free grit in either a colander under cold running water or in large bowl of cold water. Drain and pat dry.
Heat 2 tablespoons EVOO in a large skillet over medium heat. Add leeks and artichokes, sauté 5 minutes and season with salt and pepper.
Salt the boiling pasta water and drop in fettuccine.
Place zest, parsley, almonds, garlic and cheese in food processor and season with salt and pepper. Turn processor on and stream in 1/4 cup EVOO until it combines into a thick pesto sauce.