Cut off the neck of the butternut squash and peel it (save the base of the squash for another use). Cut the peeled squash neck into four ¼-inch-thick planks (save the remaining squash for another use). Set aside.
Remove the ribs from the kale leaves and discard. Chop the kale leaves. Heat 1 tablespoon olive oil in a large heavy skillet over moderately high heat. Add the kale, crushed red pepper flakes and a pinch of salt and cook, stirring occasionally, until wilted, about 3 minutes. Transfer the kale to a bowl and return the skillet to the heat.
Add the remaining 2 tablespoons olive oil to the skillet and arrange the squash planks in the skillet. Cook until the undersides are well browned, about 5 minutes. Flip the squash and continue to cook until tender and the second side is browned, about 5 minutes more.
Working in the skillet, lay the cheese evenly over 2 of the squash planks. Once it begins to melt, top evenly with the kale. Close the sandwiches with the remaining squash planks and continue to cook until the cheese has fully melted, 1 to 2 minutes. Transfer the sandwiches to plates and top with a scattering of roasted pumpkin seeds. Serve warm.