Pre-heat the oven to 350 degrees F. Place the oven rack in the center of the oven. Fill a standard muffin tin with 12 paper liners. With a hand mixer or a standing mixer fitted with a paddle attachment, beat the butter, molasses, maple syrup and vanilla on medium speed until combined. With the mixer on low speed, add the eggs one at a time. Scrape down the bowl with a rubber spatula. Add the apple juice and the pumpkin puree and beat on low speed until combined.
In a separate bowl, stir together the flour, baking powder, baking soda, salt, ginger, cinnamon and pumpkin spice or nutmeg and the cut-up apple (sprinkled with lemon juice). With a rubber spatula, gently fold the dry flour mixture into the wet butter- molasses mixture. Mix until just combined. With a small scoop or spoon, fill the 12-cup muffin tin. The batter will be overflowing out of the cups.
Bake the muffins for 35–40 minutes, or until a wooden skewer or toothpick inserted into the center comes out clean. Because the batter is moist, be sure they are fully baked. Allow the muffins to cool completely in the pan. Store at room temperature for up to 3 days, or freeze for up to 3 weeks. Inspired by Joanne Chang's Baking with Less Sugar.