Heat a large skillet over medium-low heat. Add 7 whole eggs, 5 egg whites, 1/3 cup 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 diced tomatoes, chopped ham and 1 cup Pepper Jack 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 9-inch x 13-inch 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.
Add the milk and Pepper Jack 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.
Pour the cheesy hollandaise sauce over the enchiladas and bake at 400° F for 20 minutes, or until everything is heated through.
Serve immediately topped with fresh tomatoes and green onions.
Chef's Tips & Suggestions:
If the sauce curdles (or the eggs begin to separate), add a tablespoon of boiling water and beat vigorously with wire whisk or immersion blender until it's smooth. If your stove doesn't have a burner that cooks at a low enough temperature, use a double boiler over low heat.