In a blender, whirl garlic clove until minced. Add half the bread cubes and pulse until coarse crumbs form. Pour onto a plate; repeat with remaining bread cubes. Pour 1/2 tablespoon oil into a 10- to 12-inch frying pan over medium-high heat. When hot, add crumbs; stir often, lowering heat if crumbs threaten to scorch, until crisp and golden, 10 to 15 minutes. Set aside.
Put butter and remaining 1 1/2 tablespoons oil in a 10- to 12-inch frying pan (with sides at least 2 inches tall) over medium-low heat. When butter is melted, add leeks, salt, and pepper, and stir occasionally until leeks are very limp and starting to brown, 10 to 15 minutes.
Add artichokes, 3/4 cup chicken broth, and the lemon juice; increase heat to medium and bring to a simmer. Cover; cook until artichokes are tender when pierced, about 10 minutes. Uncover and cook until liquid is evaporated and mixture begins to brown, 5 to 10 minutes longer.
Stir in wine, scraping bottom of the pan to release browned bits. Cook until liquid is almost evaporated, about 1 minute. Stir in 1/4 cup broth; if mixture appears too dry, add a little more broth.
Meanwhile, in a 5- to 6-quart pan over high heat, bring about 2 quarts water to a boil. Add linguine and cook, stirring until tender to bite, 9 to 12 minutes. Drain and stir into artichoke mixture along with prosciutto, parsley, and bread crumbs.
Trimming baby artichokes:
Cut off the stem at the base of the artichoke, using a sharp knife.
Peel back and snap off the leaves all around the base of the artichoke until you reach the tender layer of leaves that are yellow at the bottom and green at the top.
Cut off the top third of the remaining leaves (the green part). With a sharp paring knife, trim off all of the remaining green, fibrous material from around the base of the artichoke.