For the muffins:
Cover the raisins with water and bring to a boil. As soon as the water boils, turn off the heat and let the raisins sit in the water to plump for 10 minutes. Drain and pat dry with a paper towel.
Preheat oven to 400 degrees. If your figs have tough stems on them, remove them and discard. Roughly chop dates and figs. Set aside.
Use a blender or food processor to blend together the dates, figs, almond milk, applesauce, pomegranate juice, and cinnamon until very smooth. It will take 2-3 minutes to blend all ingredients to a smooth consistency, depending on the power of your blender. The end result should be similar to the texture of apple butter or smooth fruit preserves. Set mixture aside.
In a medium mixing bowl, whisk together eggs, light olive oil, sugar, brown sugar, and vanilla extract.
In a large mixing bowl, sift together flour, barley flour, baking powder, baking soda, and salt. Make a "well" in the middle of the dry ingredients. Pour mixture from the blender into the well, and then add the egg mixture to the bowl. Fold the dry mixture into the wet ingredients until the dry ingredients are just moistened and a lumpy batter forms. Do not overmix — if you do, your muffins will turn out heavy and dense. Don't worry if you see a few small pockets of unmixed flour, they will dissipate during baking. Fold plumped raisins and chopped walnuts into the muffin batter with a light-handed stir.
Prep your muffin pan by spraying a small amount of nonstick cooking spray into the bottom of each muffin tin (not the sides), or use paper muffin cup liners. Divide batter equally into muffin cups, filling each cup to the top and mounding the surface slightly. I've found that it's easiest to do this using a small ladle or an ice cream scoop.
For the topping:
If you’d like to top the muffins, mix the sugar and cinnamon together in a small bowl using a fork. Sprinkle about a ½ teaspoon of cinnamon-sugar evenly across the surface of each muffin.
Place muffins in the oven and immediately turn heat down to 375 degrees. That extra heat blast at the beginning of the baking cycle will help to activate the baking powder and soda. Bake for 23-27 minutes, until the tops of the muffins are golden brown and a toothpick inserted in the center comes out clean. Let muffins cool for 10 minutes before removing from the tin and cooling on a rack. Do not let the muffins cool completely in the tin; they are quite moist and will stick to the tin if you leave them there too long. Serve warm.