Fill a large bowl with cold water. Halve and juice the lemon, adding both the juice and the squeezed lemon to the bowl of water. Trim the stem of each artichoke to measure about 1 inch from the base. Slice 1 inch off the top of each artichoke. Snap off the tough lower leaves by bending them back to their natural breaking points. Using scissors, trim off the prickly points of the remaining visible leaves. Halve the artichokes vertically and scrape away the hairy chokes with a small spoon or paring knife. Cut each artichoke in half vertically again into 3 wedges and dunk them immediately into the bowl of lemon water. Set aside.

Heat the olive oil over medium-high heat in a large, wide pot. Add the onion and carrots and sauté until softened, about 5 minutes. Add the mushrooms and continue sautéing until the mushrooms are softened, 3 minutes more. Drain the artichoke wedges, reserving 2 cups of the lemon water. Add the wedges to the pot, stirring to coat them well with the vegetables and oil. Add the wine and sun-dried tomatoes, bring the liquid to a boil and let it reduce by half, 5 to 7 minutes.

Scatter the garlic around the artichokes and pour in the reserved 2 cups of lemon water. Season with salt and pepper, cover the pot and simmer over medium-low heat until the artichokes are tender, 25 to 30 minutes. Transfer everything to a shallow platter or serving dish. Garnish with either parsley or basil and a sprinkling of Parmesan, if desired.