In a skillet, add vegetable oil over medium heat. Press the grated potatoes between paper towels to remove excess moisture. Season with salt and pepper. Spoon the potatoes into the hot skillet, spreading them out to form an even layer. Cook until the bottom is golden and crispy, about 5-6 minutes. Flip and cook the other side until golden brown and crispy. Transfer to a plate and keep warm.

In a bowl, whisk the eggs and season with salt and pepper. Heat olive oil in a non-stick skillet over medium heat. Add onions, peppers, and mushrooms, sauté until softened. Add tomatoes and ham and saute for 1 - 2 minutes. Pour the eggs into the pan. Let the edges set, then lift them slightly to let the uncooked eggs flow underneath. Sprinkle shredded cheese over one half of the omelet. Fold the other half over the cheese and slide the omelet onto a plate.

Toast the bread slices until golden brown. Spread butter and jam.

Serve the omelet with hash browns, toast, and orange juice.