Peel off at least two layers of the outermost leaves from the artichoke and slice off the stem so the artichoke will sit upright. Slice off the top inch or so of the artichoke, then use scissors to cut the tips off the remaining leaves. Rub the lemon on all cut edges to help them from browning.
In a medium sauté pan, heat the olive oil over medium heat. Add onion and garlic; season with salt. Work the mixture for about 1 to 2 minutes, being careful not to burn the garlic. Stir in the anchovy and melt into the oil. Cook for about 2 minutes more.
Add in the breadcrumbs and reduce heat to low. Stir to bring the mix together, seasoning with salt and pepper.
Turn off the burner and then stir in cheese. Set mixture aside.
Fit a large pot with a steamer basket and fill with about an inch of water. Squeeze in the juice from the lemon half. Cover and bring the water to a medium boil so it creates steam.
To stuff the artichokes, start at the crown and peel back a petal to make a little pocket (don’t worry about stuffing innermost, light-colored leaves just above the center choke; start with the heartier leaves which are for eating). Fill the pocket with a small spoonful of the breadcrumb mix. Move to the next petal; repeat until the entire artichoke is stuffed.
Set stuffed artichoke upright on steamer basket and steam until a leaf pulls out easily. Begin checking at about 35 minutes. When done, place on serving dish alongside an empty bowl to dump used leaves.