Make the crepe batter In a large bowl, whisk together the eggs, sugar and milk. Add the flour and vanilla and whisk until smooth.
Heat an 8-inch crepe pan or nonstick skillet and rub with a little butter. Add 3 tablespoons of the batter and tilt the pan to distribute the batter evenly, pouring any excess back into the bowl. Cook over moderately high heat until the edges of the crepe curl up and start to brown, about 45 seconds. Flip the crepe and cook for 10 seconds longer, until a few brown spots appear on the bottom. Transfer the crepe to a plate. Repeat with remaining batter, buttering the pan as needed and stacking the crepes.
Make the suzette sauce In a small saucepan, simmer the orange juice with the sugar and Grand Marnier over moderate heat, stirring occasionally, until the sugar dissolves. Reduce the heat to low and gradually add the butter, swirling the pan, until it melts creamily.
Make the whipped cream In a medium bowl, whip the cream with the sugar and vanilla at low speed until it holds a firm peak.
Fold the crepes in halves or quarters and serve with the suzette sauce and whipped cream.