Preheat oven to 325º. Chop broccolini into bite-size pieces, and thinly slice green onions (both white and green parts) or garlic scapes.
Melt butter in an oven safe nonstick skillet over medium heat and sauté the vegetables until crisp-tender, about 5-10 minutes.
In a large bowl, whisk together eggs, cream, salt and pepper to taste, and cheese. When vegetables are tender, add the egg mixture to the skillet and gently combine with a rubber spatula.
Cook over medium heat, gently stirring, until the eggs are about half cooked. Transfer skillet to the preheated oven and bake until eggs are cooked through, about 20 minutes. You’ll be able to tell it’s done if you shake the skillet and the center no longer jiggles.
Serve warm, cold, or at room temperature, to suit your preference.