Preheat oven to 375°F. Grease a 9x5 or 10x5.5” loaf pan with shortening or butter and coat it with sugar. (You do this like you would grease and flour a pan. Grease it first, then add about 2 tablespoons sugar to the pan and move the pan side to side until the bottom and sides are coated with sugar. Do NOT substitute cooking spray for the butter. You can skip the sugaring and just use cooking spray, if you wish.)
Stir oil, sugar, and salt with wooden spoon or spatula. Set aside.
Add bananas, eggs, milk, vinegar, vanilla, baking soda, and pumpkin pie spice to a blender jar and blend until smooth.
Pour half the banana mixture into the oil mixture with 1 cup of flour. Stir until just incorporated, then add the remaining banana mixture and flour. Stir until just incorporated. Pour into prepared pan.
Bake for 45-60 minutes, or until a toothpick comes out clean alongside the crack. (If you put the toothpick in the crack it will come out with just a little batter/crumbs sticking to it.) The edges will be a dark brown and there will be a nice crack down the center. (There is a wide range of cooking time because all ovens bake differently, as do all pans. My banana breads never bake in the same amount of time!)
Cool completely before removing loaf from pan and frosting.
To make the frosting: whisk powdered sugar, pumpkin pie spice, and salt in a medium bowl. Whisk in vanilla and 1 tablespoon heavy whipping cream, adding more cream as needed for consistency (up to 2 tablespoons). Frost banana bread. Chill to set. Store in an airtight container for up to 3 days or slice and freeze for up to 1 month.