Grate 1 teaspoon lemon zest into a food processor. Halve the lemon.
Steam the lemon halves and artichokes in a large saucepan until a paring knife inserted into an artichoke stem meets little resistance, 25 to 35 minutes (adding more water to the pot if necessary).
Add the mint, cashews, garlic, ½ teaspoon salt, and ¼ teaspoon pepper to the food processor; pulse until finely chopped. Add the oil and process until almost smooth. Serve with the artichokes for dipping.