Set a large pot on the stovetop. Add 1-2 inches of water, and place a steam basket in the pot. Cover and set on high heat.
Trim the Artichokes: Cut the lemon into wedges. Work on one artichoke at a time. Use a large sharp knife to trim the stem, and if the top of the artichoke is pointed cut 1/2 an inch off the top, exposing the inner leaves. Then use kitchen shears to trim the points off each artichoke leaf. Now cut the artichoke in half. Use a spoon to dig the fuzzy "choke" out of the center of the artichoke halves. Make sure to get it all, but leave as much of the "heart" underneath as possible. Then quickly rub the entire surface of both halves with a lemon wedge, because artichokes oxidize and brown very quickly. Repeat with the remaining artichokes.
Once all the artichokes are prepped, place them in the steam basket. Lower the heat to a simmer. Cover the pot and steam the artichokes for 20 minutes.
Meanwhile, preheat the grill to medium-high. Place the butter and miso paste in a bowl and stir until the miso paste is worked through the butter evenly.
Move the artichokes to the grill, flat-side-down. Brush the surface with about one-third of the miso butter and salt and pepper liberally. Grill for 3-5 minutes to form charred grill marks.
Use large tongs to flip the artichokes over. Bush the surface and cavity of each artichoke with another one-third of the miso butter. Salt and pepper liberally. Grill for 3-5 minutes longer.
Remove the artichokes from the grill and brush the remaining miso butter over the cavities while they are still hot. Serve immediately.
Don't skimp on the miso butter! The extra butter pooling in the cavity of each artichoke is great for dipping the lower leaves.