Begin by preparing your ingredients for quick assembly. Break 4 large eggs into a small bowl, season generously with salt and black pepper, and beat thoroughly with a fork until well combined.
In a small frying pan, melt half of the 2 tbsp butter over high heat. Add the 2 oz (60g) of sliced shiitake mushrooms and cook for 3–5 minutes, stirring occasionally, until all the liquid has evaporated and the mushrooms are golden and tender.
Remove the pan from the heat, stir in 1 tbsp of snipped fresh chives, season with additional salt and pepper to taste, and keep the mixture hot while you prepare the omelet.
Heat an omelet pan or small frying pan over medium-high heat until very hot, then add the remaining butter and swirl the pan to coat the base and sides evenly.
Once the butter is foaming, pour in the seasoned egg mixture. Cook the omelet over medium heat, using a spatula to gently pull back the cooked edges as the eggs set, and tilt the pan to allow any uncooked egg to run toward the sides.
Continue this process until the omelet is lightly set and the underside is golden brown, then remove from the heat.
While the omelet is still warm and slightly soft on top, scatter the mushroom mixture over half of the omelet.
Fold the omelet in half to enclose the filling, then slide it onto one half of the warmed and split ciabatta loaf. The crusty bread will perfectly complement the creamy, savory omelet while providing an ideal base for serving this elegant dish.