Preheat the oven: Set your oven to 350°F (180°C) and allow it to fully preheat before baking.
Combine wet ingredients: In a large bowl, whisk together the melted butter, powdered sugar, and vanilla sugar until smooth and combined.
Add eggs and yogurt: Crack the eggs into the mixture and whisk until well incorporated, then stir in the Greek yogurt, mashed bananas, and baking soda until fully combined.
Mix dry ingredients: In a separate bowl, whisk together the flour, baking powder, and salt to distribute the leavening agents evenly.
Combine wet and dry: Gently fold the dry ingredients into the wet mixture using a spatula, stirring until just combined; do not overmix.
Fold in chocolate chips: Carefully fold the chocolate chips into the batter until evenly distributed throughout.
Prepare the pan: Lightly grease a standard 9-by-5-inch loaf pan with butter or cooking spray, or line it with parchment paper for easy removal.
Pour the batter: Transfer the batter into the prepared loaf pan and smooth the top with a spatula for even baking.
Bake: Place the pan in the preheated 350°F oven and bake for about 50 minutes, until a toothpick inserted into the center comes out with just a few moist crumbs.
Cool: Allow the bread to cool in the pan for about 10 minutes, then turn it out onto a wire rack to cool completely before slicing.