Preheat the oven to 350°F. Line a standard 12-cup muffin tin with paper liners.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, allspice and nutmeg.
Add eggs, applesauce, maple syrup, almond milk and vanilla directly to the dry ingredients. Stir until the batter is smooth and thick. Using a plastic spatula, fold in the pumpkin, walnuts and raisins until evenly distributed throughout the batter.
Pour the batter into each prepared cup to 3⁄4 full. Bake the muffins on the center rack for 25 minutes, rotating the tin 180 degrees halfway through. The finished muffins will be soft to the touch and a toothpick inserted in the center will come out clean.
Let the muffins stand in the tin for 15 minutes then transfer them to a wire rack and cool completely. Store the muffins in an airtight container at room temperature for up to three days.