For the batter: Microwave butter in 20 second intervals until melted; set aside. In a medium bowl, whisk together flour, sugar, baking powder and salt. In a large bowl, whisk the egg and milk until uniform. Sift about ½ of the dry ingredients mixture through a fine–mesh strainer over the milk mixture; whisk together until a few lumps remain. Sift remaining dry ingredients over the batter; whisk until a few lumps remain. Add the melted butter and whisk until smooth. Set batter aside while preparing ingredients for filling.
For the filling: Heat 1 tablespoon olive oil in 12–inch non–stick sauté pan over medium heat until shimmering. Add half of shallots, if using; half of spinach, and half of salt. Cook, stirring constantly until about ¾ of spinach is wilted. Remove pan from heat and continue stirring until all of spinach is wilted. Transfer sautéed spinach to paper–towel–lined plate. Repeat process with remaining olive oil, shallots, spinach and salt. Shred cheddar cheese on large holes of a box grater; set aside.
For the crêpes: Set a 12–inch non–stick skillet over medium–low heat for 3 minutes. Increase heat to medium; melt ½ tablespoon butter until bubbling subsides and butter begins to smell nutty, 2 minutes. Ladle ¼ cup batter in center of pan; lift pan off heat and tilt in circular motion to disperse batter over surface. Cook until bottom of crêpe is golden brown, about 2 minutes.
Flip crêpe; crack 1 egg slightly off–center directly onto crêpe. Using spatula, break the yolk and swirl egg around one half of crêpe. Sprinkle pinch of salt and pepper over egg, followed by about ⅛ of cheese, and ⅛ of spinach. Fold bare half of crêpe over filling; continue to cook for 1 minute. Flip crêpe over; cook for 1 minute. Serve immediately or hold in 200 °F oven until ready to serve. Continue cooking crêpes, adding more butter to pan as needed.