Whisk together eggs and milk in large bowl until light and fluffy. Crumble the goat cheese and add it to the egg mixture. Set aside.
Using a 9 inch cast iron pan over medium heat, melt butter. Add garlic, 4 cups of the arugula and tomatoes and cook for at least 5 minutes until the arugula has melted and the tomatoes soften and begin to burst. Add egg mixture and then top with remaining 1/2 cup of arugula. Allow to cook on stove for about 5 minutes.
Transfer pan to preheated oven and cook until set, about 15 minutes.