Preheat the oven to 400°F. Line a 12-cup muffin pan with liners and spray the liners with cooking spray.
In a large mixing bowl, whisk together brown sugar, honey, baking powder, baking soda, salt, pumpkin pie spice, egg replacer mixture (or the eggs), oil, pumpkin puree and milk. Mix well scraping down the sides and the bottom of the bowl.
Add the flour and mix well until combined.
Place 2tbsp of the muffin batter in each of the muffin cup, spreading to cover the bottom. Dollop a heaping tablespoon of the filling on top and cover it with 2tbsp of pumpkin batter.
Bake the muffins for 18~20 minutes or until a cake tester inserted into the edge of the muffin comes out clean.
Remove the muffins from the oven and let them cool for 5~10 minutes. Transfer them over to a cooling rack.
These muffins are best when served them on the same day. Refrigerate for 3 days or freeze for longer storage.