Bring the larger portion of vegetable broth to a boil in a large Dutch oven over high heat. Gradually add the kale, covering the pot to let each addition wilt slightly before stirring and adding more. Once all the kale is added, reduce the heat to medium-high, cover, and cook until the kale is fully wilted and the bottom of the pot is nearly dry, about 5 to 10 minutes. Transfer the kale to a bowl.

Wipe out the pot with paper towels, add the butter, and melt over medium heat. Stir in the shallots and cook until softened and translucent, 5 to 7 minutes. Stir in the garlic and pepper flakes and cook until fragrant. Pour in the remaining broth, scraping up any browned bits from the bottom of the pot, then stir in the cream and return to a boil.

Stir the kale back into the pot and cook, stirring occasionally, until the sauce has thickened slightly and clings to the leaves, 7 to 10 minutes. Remove the pot from the heat and stir in the Parmesan, nutmeg, and pepper. Serve hot with lemon wedges for squeezing over the greens.