Preheat the oven to 400°F. Line a sheet pan with parchment paper.
Mash banana with a fork until fairly smooth and no lumps are left. Add ½ cup of the banana to a 2-cup measuring cup. Add the egg to the cup with the banana and whisk with a fork until well combined.
Add enough heavy cream to reach the 1-cup measuring line. (the total amount for the banana, egg and cream will be 1 cup). Add the vanilla and stir well with the fork. Place the cup in the freezer for 10 minutes.
Place the butter in a microwave-safe bowl and cover it with a damp paper towel. Cook on high power for 50-60 seconds or just until melted. Remove from microwave and set aside to cool a bit.
In a medium-large bowl, combine the flour, brown sugar, baking powder, salt and walnuts. Make a well in the center.
After the cream has been in the freezer for 10 minutes remove and add the butter to the cream mixture, stirring with a fork until the mixture is lumpy.
Pour the banana mixture into the well in the flour bowl. Stir from the bottom up, with a sturdy spatula or large spoon, just until all of the flour is mixed in. The dough with be a little crumbly and a bit stiff.
For traditional-shaped scones, tip out the mixture onto a work surface knead it 2-3 times to bring it together. Pat the dough into a 6-inch circle.
Using a sharp knife or a bench scraper, cut the circle into 8 equal triangles. (At this point, you could freeze the triangles well-wrapped on their sheet for another day. Then bake them from frozen.)
Place the triangles onto the prepared sheet pan, spacing them with several inches in between. Brush the tops with the cream and sprinkle with sanding (or raw or turbinado) sugar.
Place scones in the oven and immediately reduce the temperature to 375˚F. Bake until the scones are golden brown and set- about 20-25 minutes. A toothpick inserted into the center of a scone should come out clean.
Transfer the scones to a wire rack to cool. Serve warm or at room temperature. Drizzle with the Brown Butter Icing, if desired before serving.
Place butter in a medium-size microwave-safe bowl. Cover the bowl with a damp paper towel then place a plate (that will cover the top of the bowl) on top of the paper towel.
Microwave on high power for 3 minutes. Continue to cook for 30-second intervals until butter is beginning to turn a medium golden brown color. This will take anywhere from 3 ½ to 6 minutes, depending on the power of your microwave.
Using a potholder or oven mitt (mixture will be HOT!) remove the bowl from the microwave and set it on a heat-safe surface. Remove the plate and paper towel and allow it to cool for 10 minutes on a heat-safe surface.a
Add 3 tablespoons of the milk and the vanilla to the butter and 1 cup of the powdered sugar. Stir with a whisk until smooth.
Drizzle over the scones as desired. You may have extra icing.
See Café Tips above in post for more detailed tips and instructions.
Adapted from The Splendid Table.