Preheat oven to 350°F. Line a muffin tin with cupcake liners.
In a small bowl, whisk flour, baking powder, baking soda, pumpkin pie spice, and salt.
In a separate bowl, mix brown sugar, yogurt, oil, egg replacer, and vanilla until combined. Gently stir in shredded carrots.
Add dry ingredients to wet ingredients and mix until combined.
Fill cupcake liners halfway full and bake cupcakes for 16-20 minutes, or until a toothpick inserted into the center of cupcakes comes out clean. Allow cupcakes to cool before removing from tin and frosting.
Using a stand mixer with the paddle attachment, beat cream cheese and butter until blended and creamy. Slowly stream in powdered sugar, continuing to beat until fully combined and smooth.