Place a medium fry pan over medium heat. Warm the butter and oil for about one minute, until the butter has melted and begins to foam.
Add the shallot and saute for three to four minutes, stirring, until soft and translucent.
Add the banana pepper and saute for another three to four minutes until softened.
Add the garlic, stir, and saute for one minute.
Add the pastirma and saute for two minutes until the fat has rendered.
Add the tomatoes, stirring to incorporate. Simmer for two to three minutes, then season with salt and pepper.
While the tomatoes are simmering, whisk the eggs in a large bowl.
Increase the pan heat to high. Add the eggs and stir them through the tomato mix, allowing them to scramble, and cook for two minutes.
Remove the pan from the heat. Sprinkle the aleppo pepper and crumble the feta over the eggs.
Serve immediately in the pan, with crusty bread on the side for dipping.
