Add olive oil to lightly coat a medium saute pan over medium-high heat. Add the garlic and swirl to release the aroma. Add the mushrooms and a pinch of salt and cook, stirring occasionally, until brown. Remove from the pan and set aside.
Add the beaten egg mixture (be sure that the mixture is smooth¿no hunks of egg white). Tilt the pan to allow the uncooked egg mixture to run to the sides of the pan to create a wide, flat "scrambled egg." Swirl the pan around occasionally to loosen the eggs from the bottom of the pan.
When the eggs are three-quarters of the way cooked through, sprinkle the middle third of the omelet with the mushrooms and goat cheese. Turn off the heat and sprinkle with the chives.
Using the spatula, fold the left third of the omelet over the filling. Press gently to secure.
Gently shake the pan to be sure that the omelet is loosened from the pan. Gently slide the right third of the omelet out onto a serving plate and flip the other two-thirds of the omelet on top. (The omelet should be folded like a letter.)
Serve the omelet with the Potato Hash. Garnish with chives.
Plunge the potatoes into boiling water, then immediately drain and place them in a bowl of ice water.
To a medium cast-iron skillet, add the bacon. Turn the heat to medium-high and cook, stirring occasionally, until the bacon has rendered. Add the onion and cook over low heat, partially covered, until translucent. Add the potatoes and cook until browned and slightly crisp.