Preheat the oven to 425 degrees . Add 1/2 stick butter to a 9-inch square baking dish and melt in the oven, about 5 minutes.
In a large bowl, whisk together the eggs and milk. In a separate bowl, whisk together the flour and granulated sugar, then whisk in the egg-milk mixture.
Pour the batter into the prepared baking dish; bake until the pancake begins to rise, 15 to 20 minutes.
Meanwhile, in a medium saucepan, cook the brown sugar, salt and 2 tablespoons water over medium heat, stirring, until bubbling, about 5 minutes. Stir in the remaining 1/2 stick butter, the sour cream and bananas and heat through.
Drizzle the pancake with half of the butterscotch sauce and sprinkle with walnuts. Slice and serve with the remaining sauce on the side.