Add 1/2 cup water and the 4 peeled and smashed cloves garlic, bay leaves and peppercorns to the insert of a 6-quart slow cooker.
Heat the butter and grated garlic in a medium skillet over medium heat until the butter is melted and the garlic starts to sizzle and become aromatic, 2 to 3 minutes. Add the breadcrumbs and 1/4 teaspoon each salt and pepper and cook until golden and toasted, about 4 minutes more. Transfer to a bowl, and let cool. Stir in the Pecorino-Romano and 1/4 teaspoon salt until well combined. Set aside 2 tablespoons of the breadcrumb mixture for garnish.
Pull off the small, tough petals near the stems of the artichokes. Cut the stems close to the base so the artichokes will stand upright. Cut off the top inch of each artichoke. Snip off any thorny tips on the remaining petals with kitchen shears. Fan out the larger leaves with your fingers.
Working over the bowl with the breadcrumb mixture, spoon the crumbs into the gaps of each artichoke until they're filled all the way around. Stand the artichokes up in the slow cooker. Cover, and cook on low until the stems are tender and the leaves come loose easily when pulled, about 7 hours. Being careful of the steam, transfer the artichokes to a serving platter, and sprinkle with the reserved breadcrumbs.
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