Gather the ingredients.

Make the crêpes: Whisk together eggs, flour, milk, sugar, and salt in a medium bowl until smooth; batter will be thick. Whisk in water, oil, and melted butter until well combined.

Heat a 10-inch crêpe pan or nonstick skillet over medium-high and brush with butter. Add 3 tablespoons batter and quickly tilt skillet to evenly distribute batter. Cook until the edges of the crêpe curl up and start to brown, about 45 seconds.

Flip the crêpe using a long spatula; cook until a few brown spots appear on the bottom, 10 to 15 seconds. Transfer the crêpe to a baking sheet. Repeat process with remaining batter to make about nine more crêpes, wiping skillet clean and lightly buttering skillet a few times as necessary between crêpes.

Make the orange-butter sauce: Process butter, ⅓ cup sugar, and orange zest in a food processor. With processor running, gradually add orange juice until incorporated.

Spoon butter mixture into a 12-inch flameproof skillet; cook over medium, stirring occasionally, until bubbling, 2 to 3 minutes. Continue to cook, stirring occasionally, until mixture is syrupy, about 3 minutes.

Reduce heat to low. Working with 1 crêpe at a time, dip both sides of crêpe in sauce using 2 forks or silicone spatulas; fold into fourths with prettiest side facing outward. Lift and let excess sauce drip off; transfer folded crêpe to a baking sheet. Repeat process with remaining crêpes, scraping down sides of skillet as needed.

Transfer folded crêpes back to skillet, overlapping slightly as needed to fit all 10 crêpes in skillet; scrape any excess sauce on baking sheet back into skillet. Sprinkle crêpes with remaining 2 tablespoons sugar.

Increase heat to medium. Add Grand Marnier and cognac; carefully ignite sauce using a long-handled lighter. Carefully spoon flaming sauce over crêpes using a long-handled, heatproof spoon until flames subside, about 30 seconds. Transfer crêpes to a platter; spoon any extra sauce over top. Serve immediately.