Heat oil in a large skillet set over medium-high heat. Tilt the pan to distribute the oil so that it covers the bottom of the skillet, add mushrooms and cook, undisturbed for 3 minutes. Season with 1/8 teaspoon salt and 1/8 teaspoon pepper and cook, stirring occasionally until golden brown, about an additional 4 minutes. Add garlic and cook until fragrant, about 1 minute. Add kale and cook until softened, about 2 minutes. Remove skillet from heat and cool 10 minutes.
6 Meanwhile, in a large measuring cup or bowl, whisk eggs, milk and remaining 1/8 teaspoon salt and 1/8 teaspoon black pepper together. Stir the sauteed mushrooms and kale into the egg mixture. Divide the egg mixture evenly among muffin cups. Top each with some of the goat cheese and bake until set and tops are golden brown, about 25 to 30 minutes.
7 Use a fork to carefully remove from the tin and garnish with chives before serving.