In a very large skillet, melt the butter. Add the bacon and cook over moderately high heat until browned on the bottom, about 2 minutes. Turn the bacon and add the whisky and brown sugar. Cook over high heat, stirring a few times, until the whisky is slightly reduced, about 30 seconds. Season with pepper and remove the skillet from the heat.
In a small bowl, beat the eggs with a pinch each of salt and pepper. Heat an 8-inch nonstick skillet. Add 1 tablespoon of butter to the skillet and pour in one-fourth of the eggs. Cook over moderately high heat, stirring, until almost set, about 20 seconds. Remove the skillet from the heat and spread the eggs in an even layer. Scatter 1/3 cup of the cheese on half of the omelet and arrange 3 quartered cherry tomatoes on top. Cook the eggs over low heat until the cheese starts to melt, about 30 seconds. Remove the skillet from the heat, and top the eggs with basil. Fold the omelet in half over the filling and slide it onto a plate. Repeat to make the 3 remaining omelets. Serve hot, with the whisky bacon.