Heat a large skillet over medium-low heat. Add 7 whole eggs, 5 egg whites, 1/3 c. milk, salt and drained green chilis to the pan. Stir constantly over medium-low heat for 4-5 minutes until the eggs start to scramble. Add the Rotel, chopped ham and 1 c. shredded cheese and continue cooking for 1-2 minutes.
Roll 2/3 cup of the ham and egg mixture into each tortilla. Place the rolled tortillas in a greased 9x13 pan.
Meanwhile, in a small saucepan vigorously stir egg yolks and lime juice with a whisk. Add 1/3 cup of the firm butter and lime zest and heat over very low heat. Stir constantly with wire whisk, until butter is melted.
Add remaining butter to the pan, continuing to stir vigorously until butter is melted and sauce is thickened. (Be sure butter melts very slowly so eggs have time to cook and thicken sauce without curdling. If your stove doesn't have a burner that cooks at a low enough temperature, use a double boiler over low heat)
*If the sauce curdles (the eggs begin to separate), add a tablespoon of boiling water and beat vigorously with wire whisk or immersion blender until it's smooth.
Add the milk and cheese to the hollandaise sauce and whisk until well combined and melted. If the hollandaise sauce had curdled at all, now is a good time to take an immersion blender to the mixture to try and smooth it out. Regardless of appearance, it will still taste good!
Pour the cheesy hollandaise sauce over the enchiladas and bake at 400° for 20 minutes, or until everything is heated through.
Serve immediately topped with fresh tomatoes and green onions.