Whisk the salt and pepper into the eggs and set aside.
Heat the oil in a 10 or 12-inch oven-safe nonstick skillet over medium-low heat. Add the onions and cook for 1 to 2 minutes until translucent. Add the sausage, increase the heat to medium, and sauté, stirring periodically, until slightly caramelized. Add the green peppers and garlic, and cook for another 1-2 minutes until fragrant. Remove from the heat.
Sprinkle the cheddar cheese evenly on top. Briefly re-whisk the eggs to redistribute the salt and pepper, and then slowly pour evenly over the cheese and vegetables. Sift or sprinkle the smoked paprika evenly over the top of the eggs.
Place the skillet in the oven and bake for 10 to 12 minutes or until the top has set (it should not jiggle).
Allow to cool briefly before slicing and serving.
If you like a bit of heat, poblano peppers would also work well!