1. Using a blender, mix 2 cups flour, 2 cups milk, 4 eggs, ½ teaspoon vanilla and ½ teaspoon salt until smooth; refrigerate.
2. In a medium saucepan, whisk together the cream, remaining 1 ¼ cups milk, ½ cup sugar and 1 pinch salt. Cook over medium heat until steaming, 2 minutes. In a medium bowl, whisk together the remaining 2 eggs and ½ cup sugar, then whisk in the remaining 2/3 cup flour until smooth. Gradually whisk half of the hot cream mixture into the flour-egg mixture, then whisk into the remaining cream mixture. Cook, whisking, over medium heat until thick, about 2 minutes; stir in the rum and the remaining 1 teaspoon vanilla. Scrape the pastry cream into a bowl and refrigerate, stirring occasionally, for 20 minutes.
4. Place a crêpe on a cake stand or flat plate; spread 1/3 cup pastry cream on top. Repeat with the remaining crêpes and pastry cream, ending with a crêpe. Refrigerate.