Preheat the Blackstone griddle over medium heat. Brush the grill with 4 Tablespoons of butter.
In a small bowl combine eggs and milk, whisk until well incorporated. Set aside.
Spread the hash browns out on the griddle and toss with melted butter. Then spread them into a rectangle, making sure they are in an even thin layer, on one half of the griddle. Sprinkle with Sweet & Smoky Rub. Allow the hash browns to cook until lightly golden brown, about 10 minutes.
On the other side of the griddle place the chopped ham and onions turning frequently until onions are translucent.
When the hash browns are golden brown on the bottom pour the egg mixture over the top. Spread evenly with the back of a spatula.
Then sprinkle 1 ½ cups grated cheese over the egg mixture.
Top with ham and onions, cook eggs 3-5 minutes or until eggs are set.
Using a large long mutual spatula, cut the rectangle of hash browns in half width wise and in half lengthwise. Slide the metal spatula underneath the hash browns to loosen them from the griddle, then fold one end of the omelets toward the other hand, folding it in half. Repeat with remaining omelets.
Top each omelet with remaining ½ cup of cheese. Turn off heat on the griddle. Once the cheese is slightly melted, remove from the griddle and serve with decided toppings.