Fill a large bowl with cold water. Squeeze the juice of 1 lemon into the bowl of water and toss the squeezed lemon wedges into the bowl of water. Set the bowl aside.
If your artichoke comes with the stems attached, trim the stem so that you have about 1 1/2 inches of stem remaining. Peel off any small leaves on the stem and around the base of the artichoke. With a paring knife or vegetable peeler, peel off the outer skin of the stem. Squeeze lemon juice on the stem and rub it around.
Using a sharp knife, cut off the top 1/3 portion of an artichoke. Then, using kitchen shears, trim off the tips of the remaining leaves to remove the thorns. Squeeze the juice from a lemon wedge over the cut side to keep the artichoke from browning.
Place the artichoke on the cutting board, cut side down, so that the stem is sticking up. Slice the artichoke down the middle. Squeeze lemon juice all over each half. You can also rub the lemon wedges on the artichokes.
Use a knife or spoon to scoop out the fuzzy choke. Be careful because the leaves right above the choke may be thorny. If they are, use kitchen shears to cut them off. Squeeze more lemon juice into the cavity where the choke once was. Place the artichokes into the bowl of water. Repeat with the other artichoke.
Heat a large pan with the olive oil over medium-high heat. When the pan is hot, add the artichokes to the pan, cut side down. Cook the artichokes for about 3 to 4 minutes. Pour the vegetable broth into the pan. There should be enough broth in the pan so that it goes up the sides of the artichoke by about 1/2 inch.
Bring the broth to boil, then reduce the heat to a low simmer. Cover the pan with a lid and let the artichokes cook for 20 to 25 minutes. The artichokes are done when a knife easily slices down the base of the artichoke, an indication that the artichoke heart is tender. Transfer the artichokes to a plate.
Pour the broth into a bowl. Return 1/3 cup of broth to the pan. Add the mandarin orange juice, mandarin orange zest, rice vinegar, sugar, salt, red pepper flakes, garlic powder, and black pepper to the pan. Stir to combine the ingredients. Heat the sauce over medium-high heat. Once the liquids start to boil, mix 1/2 teaspoon of cornstarch and water in a small bowl. Pour the slurry into the pan and stir. The cornstarch helps thicken the sauce. Let the sauce cook for another 1 to 2 minutes and turn off the heat.
Drizzle some of the sauce over the artichokes and save the rest for dipping.
The tender flesh on the insides of the artichoke are edible! The outermost leaves of the artichoke aren't too fleshy, so you may have to peel off one or two layers of artichoke leaves before you reach the fleshier ones. Use your teeth to scrape off the flesh from the leaves. Dip the leaves in the mandarin chili sauce for more flavor.