Toss tomatoes with oil and season with salt and pepper. Broil on a rimmed baking sheet for 5 minutes, or until lightly charred. While tomato cook, prepare the eggs.

Whisk eggs together with cream, chives, and salt and pepper. Melt the butter in a skillet over medium high heat. Add the eggs and stir frequently until they start to set. At this point, stir less often, gently scraping the bottom and edges of the pan to form large curds of egg. When cooked to your liking, remove from heat and serve with tomatoes and prosciutto.