Preheat oven to 350 degrees F (175 degrees C). Line 12 muffin tins with parchment or muffin liners.
In a small bowl whisk together All-Purpose Flour (1 1/2 cup), Baking Powder (2 teaspoon), Ground Allspice (3/4 teaspoon), Ground Nutmeg (3/4 teaspoon), Ground Ginger (2 teaspoon), Ground Cinnamon (1 1/2 teaspoon), Ground Cloves (1/4 teaspoon), and Salt (3/4 teaspoon). Set aside.
In a large bowl whisk together Canola Oil (1/3 cup) and Granulated Sugar (3/4 cup). Add Large Egg (2) one at a time, incorporating after each.
Whisk in Unsweetened Apple Sauce (1/2 cup), Milk (1/2 cup), and Vanilla Extract (1 teaspoon).
Whisk in flour mixture and Parsnip (2 cup) until just combined. Stir in the Pecans (1/2 cup).
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 (1/3 cup), Powdered Confectioners Sugar (1/3 cup), Milk (1 1/2 tablespoon) and Vanilla Extract (1/2 teaspoon) to form a smooth texture. Drizzle or spread onto cooled muffins and serve.