Heat a small skillet over medium heat.
Blend sugar, butter, and vanilla extract together in a medium bowl using an electric mixer until smooth and creamy. Add milk, egg, and egg yolk one ingredient at a time and mix until smooth and creamy. Add flour a little at a time until batter is smooth, making sure there are no lumps.
Lightly grease the preheated skillet. Pour 1/3 cup batter into the bowl and cook for 1 to 2 minutes on the first side. Flip and cook until golden, 30 seconds to 1 minute. Repeat with the remaining batter.
Melt butter over medium heat in a medium-sized skillet. Add bananas and cook, stirring often until soft, 2 to 3 minutes.
Melt chocolate chips and cream cheese together in a microwave-safe bowl in a microwave, 1 to 2 minutes. Mix well. Add 2 tbsp of chocolate mixture to the bananas. Set aside the remainder to use later. Mix the bananas and chocolate mixture together and let cook for 1 minute more.
Add chocolate-banana mixture to crepes; fold over and drizzle with remaining chocolate. Yields eight servings.