Heat 1 tablespoon of the butter and the olive oil in a large skillet over high heat. Add the squash and sprinkle with the salt, chile powder and pepper. Cook for several minutes, turning gently with a spatula, until the squash is deep golden brown and tender (but not falling apart). Remove to a plate and set aside.
In the same skillet, melt the remaining 1 tablespoon butter over medium-high heat and add in the kale. Toss it around with tongs and cook it for 3 to 4 minutes. Add in the cooked squash and gently toss together.