Preheat the oven to 375 degrees F. Coat a 9″x13″ baking dish with cooking spray.
Heat the olive oil in a large pan over medium high heat. Add the onions and peppers, and season with salt and pepper to taste.
Cook, stirring occasionally until vegetables are softened, 3-5 minutes.
Place the cooked vegetables, ham and hash browns in the baking dish, stir to combine.
In a medium bowl, whisk the eggs until thoroughly blended.
Add the cream, milk and salt and pepper to taste. Whisk until smooth. Stir in the cheese.
Pour the egg mixture over the ham and vegetables in the pan.
Bake for 45 minutes or until golden brown and cooked through. Sprinkle with chives. Cut into squares and serve.