Preheat the broiler to high.
To make the breakfast pizza, break the eggs into a bowl and whisk until combined. Season with a pinch of salt and pepper.
Heat a large, oven-safe skillet over medium heat. Melt the coconut oil, then add the red pepper and cook until softened. Add in the ham, cherry tomatoes, and olives and stir for 1 minute.
Spread evenly over the base of the frying pan.
Pour in the egg mixture and reduce the heat to medium-low. Cook until the base has firmed, then place under the broiler, leaving the oven door ajar, until the egg mixture is completely cooked through.
Remove from the oven, slice into wedges, and serve with some fresh basil leaves.