Place olive oil and butter in a 10 inch skillet over medium heat. Once the butter has melted, add onions and cook until they begin to caramelize, approximately 6 mins. Add garlic and cook for one minute. Add broccoli and season with pinch of salt, pepper, paprika and Herbes de Provences. Add vermouth or sherry and cook broccoli until most of the liquid has evaporated. Add sun-dried tomatoes and sauté for a couple of minutes or until the tomatoes begin to rehydrate.
In a separate bowl, combine eggs with milk, pinch of salt and pinch of pepper and beat until well combined. Pour eggs over the broccoli and sun-dried tomatoes. Sprinkle the top with the crumbled goat cheese and place in a preheated 350 degree oven for approximately 25 minutes or until the eggs have set and the top of the frittata begins to brown slightly. Remove from the oven and let sit for 5 minutes before serving.