Preheat oven to 350F, line a 9-by-9-inch pan with aluminum foil, spray with cooking spray or grease and flour the pan; set aside.
In a large microwave-safe mixing bowl, melt the butter, about 1 minute. To the melted butter, add the granulated sugar (may be reduced to 3/4 cup if you like more bitter brownies), brown sugar, egg, yogurt, vanilla, and whisk to combine. Add the bananas and stir to incorporate.
Add the dry pudding mix, cocoa powder, and stir or whisk to combine; batter will appear lumpy because of the bananas. (Note: You are not making pudding; simply add the mix as a dry ingredient. It may be omitted and add slightly more cocoa powder, flour, and granulated sugar may instead be added, to taste. I recommend using the pudding because it softens, tenderizes, and flavors the brownies)
Add the flour, baking soda, salt, and stir until just combined, taking care not to over-mix or brownies will be tougher as the gluten will over-develop. The batter is quite thick and dense, and is fluffier than typical brownie batter. Pour batter into prepared pan and bake for about 40 to 44 minutes, or until top is set and edges have pulled away slightly from sides of the pan. A toothpick inserted in the center will not come out completely clean because these are gooey, dense, and fudgy. Allow brownies to cool in pan for at least 30 minutes before slicing and serving. While brownies cool, make the glaze.
Vanilla Caramel Glaze
Note – This is a fast moving recipe; have everything in place before you begin.
In a small saucepan, melt the butter over medium-high heat. To the melted butter, add the brown sugar and bring to a boil, stirring nearly continuously. Allow the mixture to boil quite rapidly for 2 minutes, stirring nearly continuously. Remove the pan from the burner, allow it to cool for about 1 minute, and add the cream, taking caution because the mixture could bubble vigorously. Whisk aggressively to incorporate the cream and calm the bubbling.
After the bubbling has subsided, add the vanilla and whisk to combine, using caution because the alcohol in the extract could cause the mixture to bubble up again. Add the confectioners’ sugar one-half cup at a time, until desired sauce consistency is reached (I absolutely recommend using sifted sugar so the glaze whisks up smooth, silky, and free from lumps). Drizzle glaze over brownies with a spoon for a drizzly speckled effect with the white on black; or pour it over the entire top surface for a uniform thin layer of glaze (if you are using the drizzle approach, you may have excess glaze and it can be stored in the refrigerator for up to 1 month for a future baking project). Allow glaze to set up for a few minutes if desired; or slice and serve immediately. Unglazed brownies will keep for up to 5 days in an airtight container at room temperature. Glazed brownies should be stored in the refrigerator in an airtight container and will keep for up to 1 week, or can be frozen for up to 3 months. I prefer these brownies chilled and store them in the refrigerator.