Preheat oven to 400°F Whisk eggs and milk in a medium bowl. Mix in the goat's cheese; season with salt and pepper and set aside.
Heat oil in a large skillet, preferably castiron, over medium heat. Add onion and sausage and cook, stirring occasionally, until onion is softened and sausage is brown, 6–8 minutes. Microwave broccoli according to package directions and add to skillet; season with salt and pepper.
Reduce heat to low and pour reserved egg mixture over vegetables. Cook, shaking pan occasionally, until edges are just set, 10–12 minutes. Place skillet in preheated oven for 15 minutes or until center is just set.
Cut frittata into wedges and serve warm or room temperature.