Preheat oven to 350°
Add sausage to a cast iron skillet over medium-high heat, breaking the meat up as it browns, about ten minutes.
When sausage is browned, spoon out any excess liquid.
Add chopped mushrooms to the pan, cook five minutes, stirring occasionally, until mushrooms soften. Sprinkle with thyme, salt and pepper, stir to distribute seasoning, and cook an additional minute.
Remove pan from heat.
In a separate bowl, whisk eggs and milk.
Ensure that sauasge and mushroom mixture is evenly distributed in the cast iron pan. Sprinkle with goat cheese and then slowly pour egg mixture over the meat and veggies.
Move pan to oven and bake about 20 minutes, or until the eggs are cooked through.
Allow frittata to rest at least five minutes before serving.