Snap off the dark green outer leaves of the artichokes until only the pale tender inner leaves remain.
Cut off all but 1 inch of the stem. Cut off the top third of the artichoke leaves.
Using a paring knife, peel away the tough outer layer of the stem and remove the base of the leaves, leaving a smooth surface.
Cut the artichokes in half lengthwise: with a melon baller or small spoon, scoop out and discard the hairy choke and thorny inner leaves.
Cut each half in two wedges and toss them with 1 tbsp olive oil in a large bowl. Combine the vinegar and sherry with 1/4 cup water in a small dish. Set aside.
Heat the remaining 3 tbsp olive oil and garlic in a 10" saute pan over medium high heat and cook, stirring, until the garlic starts to turn golden, about 2-3 minutes. Remove garlic and discard.
Add artichokes to pan and arrange them with one cut side down. Cook until nicely browned , 3-5 minutes. Turn and cook the other cut side until also nicely browned, about 3 minutes more. Turn the artichokes on their curved side. Sprinkle the lemon zest on the artichokes and season with salt and pepper. Reduce heat to low, add the vinegar, sherry and water, cover, and simmer until the liquid has reduced to about 1 tbsp and the artichokes are tender when pierced with a fork, about 5 minutes.(If the artichokes are still undercooked after liquid is reduced, turn off heat and let sit, covered a few more minutes until they reach the desired doneness).
Remove the pan from the heat, sprinkle the thyme on the artichokes and stir well. Season to taste with more salt and pepper.
Serve immediately, or let rest uncovered, and serve slightly warm. Enjoy!.