In a medium saucepan set over medium heat, melt the butter. Continue to stir occasionally until the mixture turns amber in color and you can see brown specks in the butter (those are the flavor bits!)
Remove the brown butter from the heat and weigh it. You should be left with at least 135g. If you have a little less (2-3g), add in a little bit of water to reach 135g. If you have a lot more than 135g, return the butter to the heat to brown it for a little longer.
Pour 115g (½ c.) of the brown butter into a heat-safe bowl and reserve the remaining brown butter for the glaze. If you're making the brown butter ahead of time, cover it and place it in the fridge overnight. If you're looking for a faster process, place the butter in the freezer and stir it every 5 minutes until it has solidified.
Add the walnuts to the saucepan you browned the butter in. Set the pan over medium heat and occasionally stir the walnuts until they are toasted, then remove them from the heat and set them aside.
In a small bowl, mash the banana.
To a medium-sized mixing bowl, add the flour, baking powder, cinnamon, salt, and sugar. Cut the solidified brown butter into little chunks and add it to the bowl.
Using your fingers or a pastry blender, smush the butter into small pieces into the dry ingredients, until no large chunks of butter remain.
Add the mashed banana, sour cream, vanilla, and toasted walnuts to the mixing bowl.
Start mixing the ingredients together in the bowl. When it seems like it no longer wants to come together, transfer the dough to a clean work surface. Gently knead until the dough fully comes together.
Pat the dough down into a 6" circle. Lightly wrap or cover the scones and place them in the freezer for 30 minutes, up to overnight.
When you're ready to bake the scones, preheat the oven to 425°F / 220°C. Line a baking sheet with parchment paper or a silicone baking mat.
Cut the scones into 8 triangles and evenly spread them apart on the baking sheet. Lightly brush the tops of each scone with heavy cream or milk, then bake for 12-15 minutes, until the tops and bottoms of the scones start to turn golden brown.