3 cups Brussels sprout leaves (from about 1 pound whole)
1 shallot, minced
Fresh lemon juice
Preheat the oven to 375°F. Using a paring knife, cut the knobs off the Jerusalem artichokes. This helps them cook evenly. Cook the smaller cut-off pieces in the same pan with the large pieces and remove them when they’re soft.
Heat a tablespoon of the oil in a medium ovenproof skillet over medium-high heat. Add the large Jerusalem artichokes, salt and pepper, and cook until brown all over, about 6 minutes. Pop the pan into the oven and roast until the artichokes are tender, about 30 minutes. Roll them around every 10 minutes or so, for even roasting and browning.
Remove the skillet from the oven and put it on a burner over medium heat. Add the garlic, rosemary and butter and, using a spoon, baste the Jerusalem artichokes until they are lightly glazed and light brown all over, tilting the pan so the liquid pools at the bottom edge. Transfer to a cutting board and thickly slice crosswise.
Heat 2 tablespoons of the oil in a large skillet over medium-high heat. Add the Brussels sprout leaves, salt and pepper, and cook for about a minute, stirring constantly. Add the shallots and cook for another minute, stirring. Add the roasted artichokes and cook until the Brussels sprout leaves are brown in places and crisp-tender, about another minute. Season with lemon juice and stir in the remaining 1/2 tablespoon oil.