Melt 1 tablespoon of butter in a 6-quart pot. Add the torn chard and sauté until it wilts, about 3 to 4 minutes. Remove the chard and drain in a colander, pressing to remove the liquid.
Melt the remaining butter and sauté the leeks until soft, about 3 minutes. Add the asparagus and sauté until it starts to glisten, about 2 minutes. Return the drained chard to the pot and stir with the leeks and asparagus.
Add the heavy cream and stir. Once it’s hot, add the cream cheese and cook, stirring, until the cream cheese melts and the sauce coats the vegetables. Pour the mixture into the prepared casserole dish and sprinkle the Swiss cheese on top.
Bake in the preheated oven until the cream bubbles, about 20 minutes. Move the rack to the top third of the oven. Broil the gratin until the cheese turns light brown, about 5 minutes. Remove from the oven and allow to cool about 5 minutes, then serve.