Fill a large bowl halfway with cold water. Add the lemon juice to keep the artichokes from oxidizing, then clean the artichokes one at a time: Trim away all the tough outer leaves. Remove and reserve the stem. Cut off the spiky tops, and remove any thick fibers from the base. Quarter each artichoke heart, then use a spoon to scoop out all the hairy choke. Drop each artichoke in the lemon water before moving to the next.
Make the artichoke cream: In a large skillet over medium heat, warm 2 tablespoons of the olive oil. Add one smashed garlic clove and cook, stirring occasionally, until golden brown, 3–4 minutes. Add the artichokes stems, 8 artichoke quarters (cut sides down), and the potato. Season with kosher salt and pepper. Add 2 cups water and bring to a boil over high heat. Lower the heat to maintain a simmer, and cook until the artichokes and potato are very soft, 45–50 minutes. Carefully transfer the vegetables and their cooking liquid to a blender and blend on high until the mixture is very smooth. If it remains very fibrous after blending, press the artichoke purée through a fine sieve.
Meanwhile, braise the remaining artichokes: In a clean skillet, heat the remaining 2 tablespoons of oil until shimmering. Add the remaining garlic clove and cook, stirring occasionally, until softened, 3–4 minutes. Season the artichokes with salt and pepper, and place them, cut sides down, in the pan. Add 3 tablespoons of the wine and enough water to come three-quarters of the way up the sides of the artichokes; bring to a boil over high heat, then lower to maintain a strong simmer. Cook, without stirring, until very tender, 28–30 minutes. Remove from heat and set aside.
In a medium pot, heat 1 tablespoon of the butter over medium heat. When the foam subsides, add the shallots and a pinch of salt. Cook, stirring occasionally, until the shallots are translucent, 10–12 minutes. Add the rice and cook, stirring frequently, until fragrant and lightly toasted, 4 minutes. Add the remaining 2 tablespoons of wine; cook until evaporated. Start adding the warm stock ½ cup at a time, stirring the rice constantly and allowing the liquid to almost completely evaporate before adding more. After 15 minutes of adding stock (about 3½ cups), start adding equal amounts of the artichoke cream in place of the stock. When the rice is al dente (10–12 minutes, or after about 2 cups of the artichoke cream has been added), remove the pan from the heat. Stir in the remaining 2 tablespoons of butter and the cheese, then let the risotto rest for about 2 minutes to thicken slightly. Add more salt and black pepper to taste.
Divide the risotto among 4–6 plates. Top each with a few braised artichoke pieces, black pepper, a pinch of lemon thyme or lemon zest, and 2–3 capocollo slices. Drizzle with olive oil if desired, and serve immediately.