Wash the kale, remove the tough ribs and roughly chop the leaves.
Heat the olive oil in a large, deep pan or Dutch oven over medium heat. Add the shallots and sauté until soft and lightly caramelized, 4 to 6 minutes.
Add the kale and, using tongs, toss until slightly wilted, 3 to 4 minutes. Season lightly with salt and pepper and add the chicken broth. Cover the pan and cook, stirring occasionally, until the kale is tender, 8 to 12 minutes longer.
Raise the heat to medium high, add the butter and toss with the kale until melted. Add the half-and-half and continue tossing until the kale is thoroughly coated. Taste and adjust the seasoning as needed.