Combine the eggs, salt, flour & milk in a blender until well mixed.  Let stand for 1 hour.  The mixture should then be the consistency of heavy cream.

Heat a nonstick skillet over medium-high heat.  Brush with the melted butter, then pour 1/4 cup of batter into the skillet, swirling the pan to coat the bottom evenly.  Fully cook until golden on one side, then flip and cook 30 seconds more.  Remove to a plate and continue with the remaining batter to make a total of 8 crepes.

Heat the olive oil in a large skillet over medium-high heat, then add the mushrooms. and cook until reduced in size, stirring occasionally about 5 minutes.  Add in shallots, garlic, thyme, rosemary and butter and stir to combine, about 30 seconds.  Season with salt and pepper, and squeeze in the lemon juice.  Add the spinach and let it wilt.  Stir to mix, then remove from heat.

Preheat oven to 425°F.  Place the rack in the lowest row of the oven.

On a clean work surface, overlay two crepes by 3 inches, then spoon 3 large tablespoons of mushroom mixture in a row in the center of the crepes. Distribute 2 tablespoons of feta cheese on top of the filling.  Beat an egg in a small bowl, then brush all corners of the crepes with the egg wash.  Gently roll the crepes into a log, then roll the log into a coil shape.  Repeat with the remaining crepes and filling.

Place the rolls in a 10-inch cast-iron pan and brush with egg wash.  Sprinkle generously with the Parmesan cheese.  Gently make a divot in the center of each crepe roll with the back of a spoon.  Carefully crack an egg into each divot.  Bake for 13 to 15 minutes or until the egg whites are opaque but the yolks are still runny.  The crepes should be crispy and golden on the outside.  Sprinkle with chopped chives and salt and serve immediately.