Preheat the oven to 180 C. Whisk eggs, heavy cream and salt until you get a smooth and even texture. Set aside.
Melt butter and coat the sides of the baking dish with it. Spread vegetables evenly on the bottom of the pan.
Pour over the egg mixture. Sprinkle the cheese on top. Using a fork, distribute the cheese around a little to incorporate it into the eggs. Bake for 15 to 17 minutes, or until the edges are set and the top is lightly browned.