Using a serrated-blade knife, cut off the spiky top third of a baby artichoke and discard the trimmings.
Pull back each dark outer leaf and snap it off at the base until you reach the tender, pale green inner leaves, (this step not shown).
Use a pairing knife or vegetable peeler to remove the tough outer layers around the stem until you reach the pale layer underneath, leaving the stem attached. Cut off the tough bottom 1/4″ of the stem.
Use the paring knife to trim any remaining dark green or tough parts around the edge and underside of the artichoke and stem until it is smooth and uniformly pale in color.
Using a larger knife cut each artichoke in half lengthwise.
These tender baby artichokes with edible chokes intact can be rubbed with the cut side of a lemon half and used immediately or stored, refrigerated, for up to two days in four cups of water mixed with the juice of two lemons, which will prevent browning.
Combine the lemon juice, mustard, garlic, thyme, salt, and pepper in a large bowl.
Slowly whisk in the olive oil and set aside.
In a large saucepan, bring 1 1/2 quarts of water to a boil. Add prepared baby artichokes and cook approximately 7 to 10 minutes or until you can easily pierce them with a fork, but they still offer some resistance. Drain and immediately and immerse in cold water to stop the cooking.
When cool, brush both sides of each artichoke half with olive oil and sprinkle with salt and pepper.
Prepare Barbecue grill over a medium-hot fire, cut side down for about 5 minutes, or until the cut sides are well browned, flip and repeat.
Remove from grill and immediately drizzle with sauce.