Fill an 8-quart / 7.5 L stockpot with 2 inches of water. Add the smashed garlic, bay leaves, half the lemon juice, and 1 tsp salt. Fit a steamer basket on top and bring the water to a boil.
While the water heats, trim the artichokes. Cut off the stem so each one sits flat, then slice off the top inch with a serrated knife.
Snip the thorny tip off each remaining leaf with kitchen scissors. Rub every cut surface with the other lemon half right away so it doesn't brown.
Set the artichokes stem-side down in the steamer basket. Cover the pot, reduce the heat to a simmer, and steam for 35 to 40 minutes.
Check the water level every 10 minutes and add more hot water if it drops below the basket. The artichokes are ready when an outer leaf pulls free with almost no resistance and a knife slides easily into the base. If a leaf still fights you, give it another 5 minutes, an underdone artichoke turns the whole meal into a workout.
About 5 minutes before the artichokes finish, melt the butter in a 1-quart / 1 L saucepan over low heat. Whisk in the lemon juice, minced garlic, 1/2 tsp salt, and a pinch of black pepper.
Remove the pan from the heat and stir in the parsley. Keep the dip warm over the lowest heat setting, whisking occasionally so it doesn't separate.
Lift the artichokes out with tongs and let them rest for 5 minutes, they trap a lot of hot water in the leaves. Stand them upright on a plate, or halve lengthwise and scoop out the fuzzy choke with a spoon if you'd rather skip that at the table.
Serve warm with the lemon butter dip on the side. Pull off one leaf at a time, dip the fleshy base in the butter, and scrape it clean with your teeth.