Heat a 12-inch nonstick skillet over medium-high heat and add the butter. Add the Swiss chard and zucchini or yellow squash to the pan and season with salt and pepper. Cook until the vegetables soften, about 3 minutes.
While the vegetables are cooking whisk together the eggs and cream. Season the eggs with salt and pepper. Add the eggs to the vegetables and gently stir until they begin to set but are still runny. Top with the tomatoes and place under the broiler until golden, about 1 minute.
Slide out of the pan, slice and serve with some fresh basil sprinkled over the top.