Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving about 1-inch overhang along each side.
Whisk together flour, baking powder, baking soda and salt in medium bowl.
Place mashed banana in a large mixing bowl (or you can mash the bananas right in the bowl with a fork – you will need 360g of banana flesh which is about 3 medium bananas). Add sugar and whisk until glossy and syrupy. Whisk in melted butter. Whisk in eggs one at a time. Mix in yogurt and vanilla until blended. Add dry ingredients all at once and fold them in until just combined. Fold in chocolate chips.
Scrape batter into prepared pan and smooth it out. Bake for 40-45 minutes until the top is evenly browned and a skewer inserted into the center comes out clean. Let cool for 10 minutes, then turn out onto a wire rack to cool completely.
For the frosting, beat salted butter until smooth. Sift in cocoa powder and icing sugar then beat for 2 minutes until very pale and fluffy. Beat in vanilla extract. Add half of melted cooled chocolate and beat until combined and creamy. Add the remaining chocolate and beat until fluffy, thick and super silky.