Preheat oven to 350 degrees. Brush 12 jumbo muffin tins (each with a 1-cup capacity) with oil; set aside.
In a medium bowl, whisk flours, baking powder, pumpkin pie spice, and baking soda, flaxseed; set aside.
In a large bowl, whisk oil, pumpkin puree, yogurt, eggs, and 1 cup sugar to combine; add 1 cup walnuts and reserved dry ingredients. Mix just until moistened (do not overmix).
Divide evenly and spoon batter into muffin tins; sprinkle tops with remaining walnuts and sugar. Bake until a toothpick inserted in the center of a muffin comes out clean, 35 to 40 minutes. Cool 5 minutes in pan.