Pour 1 qt. cold water into a large bowl. Squeeze in the juice of 1 lemon. Working with a few artichokes at a time, trim off the top 1/2 inch and peel off 2 layers of outer leaves, then trim the base. cut each artichoke in half lengthwise and place in the lemon water. Preheat the oven to 450°.
Drain the artichokes well and transfer to an ovenproof, heavy, medium skillet. Add the wine and 2 tbsp. EVOO. Cover with foil, poke a small hole in the top and bring to a simmer over medium-high heat. Cook, covered, for 8 to 10 minutes, shaking the pan occasionally (the mixture will begin to sizzle when done). Uncover, lower the heat to medium and add the garlic, remaining 1 tbsp. EVOO, 1/2 tsp. salt and a few grindings of pepper. Cook, stirring often, until the artichokes are tender and browned in spots, about 5 minutes.
Meanwhile, prepare the crumb topping: In a large bowl, mix the breadcrumbs and 1/4 tsp. each salt and pepper. Finely grate in the zest of the remaining lemon. Using the large holes of a box grater, shred in the butter. Toss in the cheese and thyme, then work the mixture with your fingertips until it begins to clump.
Crumble the breadcrumb mixture over the artichokes, transfer to the upper third of the oven and bake until the topping is golden, about 10 minutes. Cut the zested lemon into wedges; serve with the crisp.