Preheat oven to 350°F / 177°C / Gas mark 4.
Line muffin tins with papers. (Or butter and flour the pan / coat with nonstick baking spray).
In a medium bowl, combine flour, baking powder, baking soda, salt, cinnamon, cardamom, ginger and pepper. Whisk to combine and set aside.
In a small bowl, combine eggs, vanilla, sugars, Hubbard squash and melted butter. Whisk to combine.
Pour wet ingredients over dry ingredients. Gently stir with a spatula until flour mixture is incorporated, making sure to scrape the bottom of the bowl.
Fill muffin liners 2/3 full.
Bake for 20 - 22 minutes, or until a tester comes out with only a few moist crumbs attached.
Let muffins cool in tin for 10 minutes before removing to a cooling rack to cool completely.
While muffins are cooling, stir together all ingredients for glaze, cover with plastic wrap and set aside. When muffins have cooled completely, glaze and top with sprinkles, if desired.