FOR THE MUFFINS: Preheat oven to 400 degrees and butter a 12-hole muffin tin. In a mixing bowl, whisk together flour, baking powder, baking soda, salt, ginger, cinnamon and nutmeg, set aside.
In the bowl of an electric stand mixer fitted with the paddle attachment, whip brown sugar with butter, 1 Tbsp vegetable oil and the orange zest on medium-high speed until mixture becomes pale and fluffy.
Blend in remaining 3 Tbsp vegetable oil and the applesauce. Add in eggs one at a time and mix just until combined after each addition while adding in 1 tsp vanilla with second egg. Stir in molasses.
Fold in 1/3 of the flour mixture in 3 additions alternating with 1/2 of the milk in 2 additions between. Fold just until combined after additions (batter will be slightly lumpy).
Divide batter among 12 prepared muffin cups, filling each well nearly full. Bake in preheated oven 8 minutes then reduce oven temperture to 375 and continue to bake 8 - 11 minutes longer until toothpick inserted into center comes out with a few moist crumbs attached.
Remove from oven and run a knife around muffins to remove and transfer to a wire rack to cool slightly.
When muffins are slightly warm, dip into glaze or spread over tops, then return to cooling rack and allow glaze to set at room temperature. Store in an airtight container.
FOR THE GLAZE: In a mixing bowl, whisk together powdered sugar, vanilla and enough orange juice to make a smooth glaze.