Make the hash browns: In a large skillet on medium heat melt butter. Meanwhile, place shredded potato in a towel and ring out excess moisture. Add potatoes to skillet, spreading out evenly. Once crisp on bottom, about 8 minutes, flip and crisp up other side. Season with salt and pepper. Remove from pan and set aside.
Make omelette: Add butter to pan and spread to coat bottom. Pour in eggs and sprinkle with salt and pepper. Cover and allow to cook and set.
Once set, layer one side with cheese, hash brown, chorizo, caramelized onion and poblano. Carefully fold other side over filling. Cover and cook an additional 2 minutes.
Slide or invert omelette onto a plate and slice. Top with fresh pico de gallo and serve.