Preheat oven to 350F, spray a 9-by-5-inch loaf pan with cooking spray with flour (I use Pam for Baking) 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 sugars, eggs, vanilla, yogurt, and stir or whisk to combine. Add the bananas and stir to incorporate. Add the dry pudding mix and stir to combine (Note: You are not making pudding; simply add the mix as a dry ingredient. You don’t have to use pudding mix but it creates wonderful moisture and flavor in the bread. If omitting, you may wish to add an additional 1/4 cup granulated sugar and an additional 1/4 to 1/3 cup flour, based on taste preference and how your batter looks).
Add the flour, baking soda, salt, and stir until just combined, taking care not to over-mix or bread will be tougher as the gluten will over-develop. Pour batter into prepared pan and bake for 50 to 58 minutes, or until top is golden and set, and a wooden skewer, cake tester, or knife inserted in the center comes out clean. If bread is browning too fast on the top, you may wish to lower your oven temperature to 325F midway through cooking, at about the 30-minute mark if your oven runs hot or tent the pan with foil in approximately the last 20 minutes of cooking. Allow bread to cool in the loaf pan for at least 20 minutes before removing from the pan and transferring to a rack to finish cooling.
You can brown the butter in a small saucepan on the stovetop, heating over medium heat. Swirl the pan or stir frequently for about 5 to 7 minutes, until the sputtering, crackling, and foaming has subsided, the butter has browned, and has a nutty aroma. Watch it closely so that it doesn’t go from browned and nutty to burnt and inedible.
Or, brown the butter in the microwave in a microwave-safe bowl by heating it on high power, uncovered, for 5 to 7 minutes, until the sputtering, crackling, and foaming has subsided, the butter has browned, and has a nutty aroma. The same rules apply in the microwave as on the stovetop; watch it closely and start checking it every 15-to-30 seconds starting at about the 5-minute mark, so that it doesn’t go from browned and nutty to burnt and inedible.
Transfer hot butter to medium-sized mixing bowl and allow it to cool for about 10 minutes. Add the confectioners’ sugar, vanilla, and whisk to combine. Based on desired glaze consistency and taste preference, add the cream one tablespoon at a time, until desired consistency is reached, playing with sugar and cream ratios as necessary. (I only use butter, sugar, vanilla in this glaze, no cream). Drizzle glaze over the top of the bread before slicing and serving; or slice, serve, and glaze each piece individually. I prefer to use the glaze like butter and spread it liberally on the interior surface of a slice.
Store unglazed bread in an airtight container at room temperature for up to 5 days or store glazed bread in the refrigerator for up to 5 days. Unglazed bread can be frozen for up to 3 months.