Preheat a grill to medium. Fill a large bowl with cold water and squeeze in the halved lemon; reserve the halves. Remove the outer dark green leaves from the artichokes until only light green and yellow leaves remain. Cut off the top 1/2 inch of the artichokes. Using a paring knife, trim the stem and lightly peel around the bottom of the base where it meets the stem. Cut the artichokes in half, rub with the lemon halves and add to the lemon water.
Make the salsa verde: Combine the mint, parsley, chile pepper, capers, anchovies, garlic and mustard in a medium bowl. Stir in the lemon juice and 6 tablespoons olive oil to make a thick, chunky sauce; season with salt. Set aside at room temperature.
Drain the artichokes and pat dry. Toss the artichokes in a large bowl with the remaining 2 tablespoons olive oil; season with salt. Grill the artichokes, turning occasionally, until tender and charred in spots, 6 to 10 minutes, depending on their size. Toss with the salsa verde while still warm.