Remove 4 1-inch strips of zest from the lemon. Cut the lemon in half and juice ¼ cup of juice. Reserve the used lemon halves. Combine the lemon juice, strips, and oil in a large saucepan. Set aside.
Use a chef's knife to, one at a time, cut off the top third of each artichoke, cut away the woody part of the step, and peel the fibrous outside away from the stem. Snap off the tougher outer leaves until you get to the more tender inner ones. Cut the artichoke in half lengthwise and rub each half with the juiced lemon. Plate cut-side-down in the saucepan.
Add the garlic, pepper, salt, thyme, and rosemary or mint to the saucepan. Bring to a boil and reduce to a simmer, stirring occasionally, for 5 minutes. Remove the pot from the heat, cover, and let stand for 20 minutes or until the artichokes are tender.
Use a slotted spoon to transfer the artichokes to two sterilized pint jars. Do not add the thyme, rosemary, or mint sprigs to the jars. Strain the oil and pour it over the artichokes, leaving ½-inch head space. Allow to cool to room temperature and then transfer to the fridge. The artichokes will keep for up to 3 weeks.