1. In a mixing bowl, whisk together chickpea flour, water, turmeric, salt, and black pepper until smooth.
2. Heat olive oil in a non-stick skillet over medium heat. Add sliced mushrooms and sauté until tender.
3. Pour the chickpea batter into the skillet, spreading it evenly. Cook for about 5-7 minutes until the edges start to lift.
4. Sprinkle the vegan Swiss cheese over one half of the omelette. Fold the other half over the cheese and cook for another 2-3 minutes until the cheese melts.