Preheat oven to 400°F. Place squash in a baking dish filled with ½ inch of water, and cover. Cook until flesh is soft when pierced with tip of a paring knife.
Scoop out squash flesh and purée in blender or food processor. Cool. Squash can be prepared up to 1 day ahead.
For the muffins, preheat oven to 350°F. Grease muffin pan, then add liners.
In a small saucepan over medium heat, melt butter, and set aside in warm place so it stays liquid.
In a large mixing bowl, combine flours, baking powder, baking soda, spices and salt.
In a separate bowl, whisk butter, sugar and vanilla until combined.
Whisk in eggs, then add milk, yogurt and squash purée. Add dry ingredients and whisk to combine. Pour batter into muffin tin. Bake for 15 minutes, rotate pan, and bake for another 15 minutes, or until inserted toothpick comes out clean.