Melt the butter in a large skillet over medium heat, and cook and stir the onions until translucent but not browned, about 8 minutes. Mix the cooked onions and the butter from the skillet with the rice, and stir in the half-and-half, salt, and 1 3/4 cup of the Swiss cheese. Transfer the mixture to the prepared baking dish, and sprinkle the remaining 1/4 cup of Swiss cheese over the top.