Preheat the oven to 350°F.
Place the butter in a skillet over medium heat and allow it to melt. Add the chopped pecans and cook, stirring from time to time, for 2 to 5 minutes, until fragrant and lightly browned. Remove them from the heat and let them cool.
In a large bowl, stir together the all-purpose flour, whole wheat flour, oats, baking powder, salt, cinnamon, and brewer’s yeast until the mixture is evenly blended.
In a separate bowl, whisk the egg with the granulated sugar, brown sugar, vanilla extract, and melted coconut oil until smooth and thoroughly combined.
Add the dry mixture to the wet mixture gradually, stirring until a uniform dough forms.
Fold in the grated carrots, raisins, and cooled toasted pecans, mixing just until they are distributed throughout the dough.
Portion the dough into tablespoon-sized scoops onto an ungreased baking sheet. Flatten each portion slightly to form round cookie shapes.
Bake for 8 to 10 minutes, or until the cookies are set and lightly golden.
Let the cookies rest on the baking sheet for a few minutes after baking, then transfer them to a wire rack to cool completely.