Spread walnuts on an ungreased sheet pan and bake at 350°F degrees for 6-8 minutes. Cool completely, then roughly chop. Cool and store if not using right away.
In a large mixing bowl, combine 1 cup of the flour and the yeast.
In a small saucepan, heat the milk, sugar, butter and salt to 110-115 °F. Add the milk mixture to the dry mixture along with the mashed banana and the egg.
Beat 3 minutes, or until smooth. Stir in the remaining flour (1 1/2 - 2 cups), enough to make a stiff dough (dough should not stick to hands).
Turn out onto a floured surface and knead 6-8 minutes, or until elastic and smooth. Alternately, knead with the hook attachment on a stand mixer for 2 minutes on the stir setting.
Place in a greased bowl, cover and let rise until double. Alternately, can cover and place in refrigerator for 12 hours - overnight.
Punch down dough and turn out onto a floured surface. Roll the portion of the dough into a large rectangle.
In a small mixing bowl, combine the dark brown sugar, cinnamon and chopped walnuts.
Using a pastry brush, brush the dough with the melted butter. Evenly sprinkle the cinnamon sugar mixture on top of the dough.
Roll the rectangle up and cut into 12 rolls; place rolls in to a prepared 8” baking pan. Cover and allow the rolls to rise in a warm place until double in size, around 1 hour.
Bake at 375°F for 25-30 minutes, or until the edges of the rolls become golden.
Allow the rolls to cool on a wire rack until warm; combine the ingredients for the glaze, adding enough water to make it a drizzling consistency. Drizzle over warm, but not hot, rolls. Sprinkle with chopped walnuts.