NOTE: This recipe makes one omelet at a time.  Follow the steps for one omelet and then repeat to make four total. 

1. In a medium mixing bowl, crack 3 eggs and whisk thoroughly to combine.  It should be one homogenous mixture, with no streaks of egg white running throughout.  Stir in 1 tablespoon of chives and a pinch of salt and pepper.
2. Preheat a large 12-inch skillet over medium heat.  Melt 4 tablespoons of butter; once melted, add the wine and mustard and whisk to combine.  Bring to a simmer and cook until most of the liquid has evaporated, about 3 minutes.  Add the bread cubes and toss to coat in the mustard mixture.  Cook, stirring occasionally, until the bread cubes begin to turn golden and crisp, about 3 to 4 minutes.  Transfer to a plate and set aside.
3. Preheat an 8-inch nonstick skillet over medium heat and add 1/2 tablespoon of butter.  Once butter has melted, swirl to coat the pan and pour the egg mixture into the center.  Using a rubber spatula, draw the edges of the egg mixture in toward the center, allow the uncooked egg to run around the cooked part.  Continue this process until the eggs are soft but set, about 2 minutes.  Remove the pan from the heat and scatter 1/4 cup cheese over the omelet.  Cover and let stand for about 2 minutes, until the cheese has melted.  Scatter about one-quarter of the bread cubes on one side of the omelet and use the rubber spatula to fold the unfilled half over top.  Sprinkle additional chives and a pinch of flaky sea salt over the top, if desired.
4. Repeat the process with the remaining ingredients to make four omelets in total.