Preheat oven to 350℉ and line 12 muffin tins with parchment or muffin liners. In a small bowl whisk together flour, baking powder, spices and salt. Set aside.
In a large bowl whisk together oil and sugar. Add eggs one at a time, incorporating after each. Whisk in applesauce, milk and vanilla to combine. Whisk in flour mixture and parsnips until just combined. Stir in pecans.
Divide batter equally between prepared muffin tins using a generous 1/4 cup of batter each. Bake in preheated oven for 25-28 minutes until a toothpick inserted comes out clean. Remove from oven and allow to cool for 5 minutes. Remove to a cooling rack and allow to cool to room temperature.
In a small bowl stir together cream cheese, icing sugar, milk and vanilla to form a smooth texture. Drizzle or spread onto cooled muffins.