Take a medium-large oven proof pan and place on medium heat. Add 1 tbsp of the oil, allow to heat up for a minute and toss in the halloumi. Cook until a bit browned while tossing frequently. Remove from the pan and keep aside.
In the same pan add the remaining 2 tbsp of oil and allow to heat up for a minute. Add the pumpkin cooking for about 10’ to soften. Season with the salt and pepper, add the peppers and cook for further 2’.
Then add the halloumi, pour the balsamic vinegar, add the mint and the whisked eggs. Give it a gentle stir and cook for about 5’ so that the base of the omelette is set.
In the meantime, turn on the oven to max temperature, broiler/grill on and place inside the pan with the omelette. Cook for about 5’ until the omelette is puffy and golden browned.
Remove from the oven, allow to cool for 5’ and place the omelette to a large plate. Cut and serve.