I made my own "Egg McMuffin" using my very small Lodge 3.5 inch skillet. Flipped it over onto a Griswold #3 to fry the second side. Too bad I didn't have some sausage to make it a Sausage McMuffin! But with just scrambled eggs, American cheese and a toasted English Muffin (buttered), it wasn't too bad!
I start out with oil in the small Lodge skillet. Usually, it's too much oil in there, so then I drain it by dumping out the heated oil onto the Griswold #3. After the egg has set up in the small Lodge, I flip the egg onto the oiled Griswold. I could use butter, but since I butter the English muffin, I don't bother to butter the skillets and use vegetable oil instead. I found the key is to use low to medium heat on the skillets (like any other cast iron). I used a medium sized egg, but I really think even a small sized egg would work for an Egg McMuffin. I use a small silicone spatula to help guide the egg out since my other metal spatulas are too large.
Photos taken with an Apple iPhone 6s+
Below is a comparison of the Lodge 3.5 inch skillet to a Griswold #3 and Griswold #8 skillet. Plus, I had to take a photo of the 3.5 inch skillet with a sunny side up egg in it too... just so it looks like the Lodge logo! There's also a photo of one that I made with a ham slice, so honey mustard for sauce, an egg, cheese and an English muffin. Not bad!