Beat eggs, milk, seasoned salt, salt, and black pepper together in a bowl.
Heat olive oil in a large non-stick skillet over medium-high heat; saute jalapeno in hot oil until slightly softened, 2 to 3 minutes. Add ham to jalapeno and cook until heated through, about 1 minute.
Pour egg mixture into ham mixture. Cook and stir until eggs are set but not dry, 3 to 5 minutes. Sprinkle 1/2 of the Cheddar cheese over eggs; cook and stir until cheese is melted. Transfer eggs to a plate and sprinkle remaining cheese over the top.
