Preheat the oven to 350°F. Line 12 muffin cups with cupcake liners.
In a large bowl, stir together the flour, sugar, baking powder, baking soda, pumpkin pie spice, and salt.
In a medium bowl, whisk together the pumpkin puree, maple syrup, egg, melted butter, and vanilla extract.
Add the wet ingredients to the dry ingredients, and stir until just combined. Be careful not to over mix.
Use an ice cream scoop to divide the mixture between the muffin cups.
Bake for 25 to 28 minutes, until a toothpick comes out clean.
Transfer the muffins to a wire rack to cool slightly.
When the muffins are slightly cooled but still warm (about 15 minutes), whisk together the sugar, maple syrup, and maple extract in a small bowl.
Add water or milk 1 teaspoon at a time as needed to adjust the consistency.
Drizzle over the muffins and serve.