Crack eggs into a large mixing bowl. Add goat milk, salt and pepper and whisk until thoroughly combined.
Heat olive oil over medium in a medium-sized cast-iron skillet or other ovenproof skillet.
Add leeks and sauté until leeks begin to soften, about 5 to 8 minutes. Add mushrooms.
Continue to sauté until mushrooms have released their fluid and are soft, about another 5 to 8 minutes.
Pour egg mixture over the sautéed vegetables and stir to combine. Allow to cook on the stovetop for 3 or 4 minutes. Sprinkle feta over the top of the eggs, pushing the cheese into the egg mixture so it is submerged.
Place in the oven and bake for 15 minutes. The top of the frittata should be golden yellow and a toothpick inserted in the center should come out clean.