Bring a large pot of water to a boil for the pasta.
On a work surface, using the flat side of a chef's knife, crush the olives [1]. Pull out the pits [2], then chop the olives [3].
Heat a large skillet over medium to medium-high. Add the olive oil, two turns of the pan. Melt the butter into the oil. When the butter foams, add the artichokes and leeks; cook, stirring often, until the leeks soften, 2 to 3 minutes. Add the thyme, garlic and lemon zest. Season with salt and pepper; stir until the garlic softens, 1 to 2 minutes. Add the olives, stock and wine; reduce the heat to low. Let the sauce simmer, stirring often, while the pasta cooks.
Salt the boiling water, add the pasta and cook until almost al dente. Reserve a ladle of the starchy cooking water; drain the pasta. Toss the pasta, cooking water, lemon juice, 1/3 cup cheese and the tarragon with the sauce; season. Drizzle with EVOO. Pass more cheese at the table for topping.
The Gotta-Know Guide to Olives
