Position oven rack in the center and preheat to 350°F (175°C). Line a 9x5-inch loaf pan with parchment paper, leaving overhang on the long sides, or grease thoroughly with butter or baking spray.
Peel the ripe bananas into a large mixing bowl and mash with a fork or potato masher until mostly smooth, leaving a few small lumps for texture. You should have about 1½ cups mashed banana.
Add the melted butter, brown sugar, and granulated sugar to the bananas and whisk vigorously for 1 minute. Add the eggs one at a time, whisking after each, then whisk in the Greek yogurt and vanilla until smooth and creamy.
In a medium bowl, whisk together the flour, baking soda, salt, and cinnamon for at least 30 seconds until evenly combined and lump-free.
Pour the dry ingredients over the wet mixture and fold gently with a rubber spatula just until no flour streaks remain — do not overmix, as this leads to dense bread.
Reserve 2 tablespoons each of walnuts and chocolate chips for topping, then fold the remainder into the batter with just a few strokes until evenly distributed.
Pour the batter into the prepared pan and smooth the top with the spatula. Sprinkle reserved walnuts and chocolate chips over the top and gently press them down slightly.
Bake for 60–70 minutes until the top is deeply golden, a toothpick inserted in the center comes out with just a few moist crumbs, and an instant-read thermometer reads 200–205°F (93–96°C). Tent loosely with foil after 45 minutes if the top is browning too quickly.
Cool the bread in the pan on a rack for 15–20 minutes, then use the parchment overhang to lift it out and cool for at least 30 more minutes before slicing with a sharp serrated knife.