Preheat your oven to 400°F and line a small baking sheet with parchment paper.
Dice the yellow potato into 1/2-inch cubes and toss them in a bowl with the extra virgin olive oil and half of the sea salt and black pepper.
Spread the potatoes in a single layer on the baking sheet and roast for 20-25 minutes until the edges are crisp and golden.
While the potatoes roast, thinly slice the cremini mushrooms and finely mince the garlic clove.
Heat a non-stick skillet over medium heat with half of the ghee, then sauté the mushrooms and garlic until the mushrooms are caramelized and deep brown.
Remove the mushroom mixture from the pan and set aside; whisk the two large eggs in a small bowl with the remaining sea salt and black pepper.
Melt the remaining ghee in the skillet over medium-low heat and pour in the whisked eggs, letting them sit for a moment to set.
Use a spatula to gently lift the edges of the omelet, allowing the raw egg to flow underneath until the top is mostly set.
Sprinkle the shredded Swiss cheese and sautéed mushrooms over one half of the omelet, then fold the other half over the filling.
Cover the pan for 30 seconds to ensure the cheese is fully melted, then slide the omelet onto a plate and serve with the roasted potatoes and a garnish of fresh chives.