Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring the water to a boil. Add the kale, cover, and steam until just tender, 7 to 10 minutes.
Heat olive oil and butter in a large skillet over medium heat; cook and stir onion, celery, mushrooms, green bell pepper, and garlic in the oil and butter mixture until the onion is tender, about 5 minutes. Stir kale and rice into the mixture, breaking the rice into grains with your spoon as you stir; season with dry mustard, cayenne pepper, salt, and black pepper. Cook and stir until the rice is hot, about 5 minutes.
