Preheat oven to 425 degrees F (220 degrees C). Lightly grease a 2-quart casserole dish.
Heat olive oil in skillet over medium heat; cook and stir onion and garlic until onion is softened, about 5 minutes. Add curry powder, turmeric, ginger, and cayenne pepper; stir to coat. Add kale; cover and simmer, stirring occasionally, until kale is tender and wilted, 5 to 10 minutes.
Cover the bottom of the prepared casserole dish with a layer of potato slices; top with a layer of kale mixture. Season with salt and black pepper. Continue layering with remaining potatoes and kale mixture, ending with a potato layer. Pour melted butter over top layer of potatoes.
Bake in the preheated oven until potatoes are tender and slightly browned around the edges, about 35 minutes. Sprinkle with Cheddar cheese and cook until cheese is melted, 3 to 5 minutes.