Heat olive oil in a pan over medium heat; add onion and green pepper. Cook and stir until onion is slightly brown, about 5 minutes. Stir in ham and garlic salt.
Beat eggs, asparagus, and milk together with a whisk or a fork in a bowl; pour over ham mixture. Add whole Provolone cheese slices or break them into pieces. Cook until eggs begin to set, about 3 minutes. Gently fold the omelet in half; cook until cheese melts, about 2 minutes.