Preheat oven to 350 F. Grease a 9x5-inch loaf pan; set aside.
In a large bowl, beat bananas until mashed.
Add butter and sugar, and beat until well-combined.
Mix in egg and vanilla.
Add flour, baking soda, and salt; stir in until just incorporated.
Bake for 45-55 minutes, or until a toothpick inserted in the center comes out clean.
Let cool in pan for 10 minutes, and then remove to a wire rack to finish cooling.
To make the glaze, add butter to a heavy saucepan.
Cook butter over medium heat until it starts to foam, stirring frequently.
Stop stirring, and let it continue to cook until amber brown.
Remove from heat, and stir in powdered sugar and enough milk to make glaze desired consistency. If your powdered sugar is lumpy, sifting it will help make the glaze smoother.