I would probably use milk instead of an egg dip. Main reason is you should save your eggs for a better purpose.
If the steaks are more than an inch thick you want to butterfly them, or just completely cut them in two.
Flour, dip, flour, fry.
Potatoes. Dice 3 raw potatoes (about cubed sugar size). Should give you about 3 cups. Bring a pot of water to a boil and put in the potatoes, I know your stove top has pretty much one setting but if you can keep it to a "low" boil, that would be best. Cook the potatoes for about 10- 15 minutes, you want them soft but still firm.
Strain the potatoes and put them in an oven safe dish, pan, whatever you have. In the pan you used for the potatoes, melt about 2 tbls of butter. Add about 3 tbls of flour and stir to blend it well. Start gradually adding a little milk while stirring, in all you're going to use about a cup to a cup and a half of the milk. Keep cooking and stirring until it gets smooth and thick (like the consistency of a cream of whatever soup). Then add about a cup of the cheese a little at a time until it's melted.
Pour the sauce over the potatoes and mix it gently, don't want the potatoes all mashed and broken.
If you have some bread crumbs, sprinkle them on top and drizzle them with olive oil and a little garlic salt.
Bake in the oven at 400 degrees for about 8-10 minutes just to heat it through.
Green beans would compliment this meal.
*Adding garlic to any of the above would be great.