For the cupcake batter, sift flour, baking powder, baking soda, spices and salt into a medium bowl and whisk to blend evenly.
Combine grated carrots and both sugars in a large bowl. Let stand for no more than 3 minutes to allow the sugar to break down the carrots and release some liquid. This helps to soften the carrots slightly so that they don’t become stringy bits in your cakes. Whisk in eggs until well blended, then whisk in oil, yogurt and vanilla. Add flour mixture and pecans and fold gently using a spatula until mostly incorporated, but do not over mix.
Divide the batter evenly among paper liners filling them about ¾ full. Bake for 17-20 minutes until cupcakes are golden and they spring back when pressed gently. Transfer muffins to a wire rack to cool completely.
For the frosting, beat soft butter with soft cream cheese until smooth. Add sifted icing sugar and beat until smooth and fluffy. Beat in yogurt one tablespoon at a time until creamy and then beat in beat in lemon juice and vanilla.
Spread about 2 tablespoons of frosting over each cooled cupcake and then top with chopped toasted pecans.