In Malaysia, a common breakfast is roti telur + teh tarik which is close to the dark breakfast region. It's like paratha, with an egg, and milk tea.
It is difficult to put milk into food. Why not just drink it? Alternatively, can we drink eggs and flour?
Cheese is another variation for milk. What about grilled cheese and eggs? Or some variation on Mac and Cheese?
You can also consider other dimensions like vegetables and spices. According to this plane, shakshuka is pure egg. Add spices to milk and you have chai. Add eggs to chai and you have cursed eggnog.
Egg paratha is a common Indian dish. The dough can be made with flour and water, but is traditionally made with flour and milk.
https://www.thedeliciouscrescent.com/omelette-stuffed-parath...
Roti Telur is basically Egg Paratha. Indian migrants brought Paratha to Malaysia and Singapore, and it underwent some "localization" to suit the local palate, including being drenched in palm oil as it is cooked on the flat griddle. Sure fire way to clog your arteries, if eaten on a daily basis.
The palm oil makes the difference. Not exactly drenched, but just enough for the crispy Mallard reaction.
It's a little simpler than the given recipe too. Just a regular paratha, crack an egg directly onto it, then cook on a griddle.
There is prior art in the grilled cheese and eggs area: Denny’s Moons Over My Hammy.
Or the even more legendary Breakfast Dagwood https://violasmithcooking.blogspot.com/2009/08/breakfast-dag...
For a continental vibe see the french "Croque Madame"
Is that different than a "Croque Monsieur"? For whatever reason I've been watching Jacques Pépin videos recently. The crust on his "Croque Monsieur" is incredible.
https://youtu.be/2ZTOUyUBCz4
We can certainly drink eggs, Rocky had a few in the morning before he went to punch hanging frozen meat.