In a large bowl, whisk the eggs and cream together and season with salt and pepper. Set aside.
Heat the oil in a large ovenproof skillet over medium high heat. Add the garlic, onion, peppers and chorizo. Cook for 4-5 minutes until the onion and peppers are soft and the chorizo is completely cooked through.
Reduce heat to medium low. Add the eggs and tomatoes to the pan and stir until just combined.
Move pan to oven and bake for 10-12 minutes, or until just set. Sprinkle the cheese on top and bake for another 5 minutes until egg has fully set and cheese has melted. Top with parsley and cilantro leaves.