Whisk flour, beer, eggs, 2 tablespoons vegetable oil, nutmeg, and salt in a large bowl to form a smooth batter.
Toss bananas with enough lemon juice to coat in a separate bowl.
Beat the cream cheese and brown sugar together in a separate bowl until light and fluffy; fold whipped topping into cream cheese mixture to form the cheese filling. Set aside.
Heat white sugar in a saucepan over medium heat, stirring constantly, until melted and brown, 2 to 4 minutes. Remove sauce pan from heat and stir boiling water into melted sugar. Return to heat and stir until it forms a smooth and clear syrup.
Whisk cornstarch and 1/2 cup water together in a small bowl; add to syrup in saucepan. Simmer over low heat, stirring constantly, until thick and clear, 5 to 7 minutes. Whisk butter into syrup to form a caramel sauce.
Heat 1 teaspoon vegetable oil in an 8-inch crepe pan over medium heat. Pour about 1/4 cup crepe batter into heated oil. Tip and rotate the skillet until batter covers the entire area. Cook until the batter turns from wet to moist, and the edges begin to curl away from the sides of the skillet. Flip crepe and continue cooking until lightly golden on the other side. Place crepe onto a plate, and cover with a kitchen towel to keep moist. Repeat with remaining batter, lightly oiling the skillet as needed with 1 teaspoon vegetable oil each time to keep the crepes from sticking.
Assemble crepes by spreading about 2 tablespoons caramel sauce over each crepe. Spread 1/8 the cream cheese filling onto the caramel layer; top with 1/8 the bananas. Roll the crepe around the bananas and place seam-side down on a serving platter. Repeat with remaining crepes and ingredients. Drizzle remaining caramel sauce over crepes.