Heat a tablespoon of olive oil in a skillet over a medium/ high heat. Add the bacon and cook through until golden and crisp at the edges. Remove from the pan with a slotted spoon and set to one side.
Step 2
Thinly slice the onion and add to the skillet with the bacon grease, balsamic vinegar and erythritol. Stir well to combine and cook over a low/medium heat for 5-6 minutes or until soft and caramelized.
Step 3
Whilst the onions are cooking, crack the eggs into a mixing bowl and season with salt and pepper. Beat together to combine.
Step 4
Remove the onions from the skillet and set to one side. Wipe the skillet clean and heat the remaining oil over a medium heat. Pour in the beaten egg mixture. Allow to settle and cook through. Once the edges are cooked, ease them away from the sides of the skillet with a spatula and allow any uncooked egg to flow underneath.
Step 5
Once the omelette is cooked, carefully slide onto a large plate and crumble the brie over one half.
Step 6
Roughly tear the bacon over the cheese and scatter over the balsamic onions. Fold in half to serve.