Heat a small skillet over medium heat. Toast pecans until they become fragrant, about 6-8 minutes. Transfer to cutting board to cool.
Return skillet to medium heat, and cook butter, stirring often until golden brown, about 4-5 minutes. Transfer to a medium heat proof bowl to cool.
Coarsely chop ¼ cup of the dried cranberries and transfer to a small bowl. Coarsely chop the toasted pecans and mix ¼ cup of them with the chopped cranberries.
Move oven rack to the middle position and heat oven to 375°F. Grease the cups of a 12 cup muffin pan with any remaining browned butter from the skillet, or with canola oil.
Whisk applesauce, buttermilk (or kefir), eggs, and vanilla into the browned butter. In a large bowl, whisk together the all purpose flour, whole wheat flour, baking powder, baking soda, cinnamon, allspice and salt. Gently stir in butter mixture with a large silicone spoon or spatula. Fold in sweet potato, reaming 1 cup of dried cranberries and remaining ½ cup of the toasted pecans until incorporated.
Divide batter equally among 12 muffin cups. Top each muffin with a portion of the chopped cranberries and pecans. Bake until golden brown and a toothpick inserted into the center of a muffin comes out with moist crumbs attached, about 18-20 minutes.