Preheat oven to 350°F. Line two cookie sheets with parchment paper or silicone baking mats.
In a small bowl, whisk flour with baking soda, cinnamon and salt. Set aside.
Cream butter and brown sugar in a large bowl with an electric mixer 1-2 minutes. Mix in egg and vanilla until smooth.
Add dry ingredients to wet and mix until smooth. Stir in carrots and nuts.
Scoop 2 tablespoon size balls onto cookie sheets 2-inches apart. Lightly flatten with the palms of your hand.
Bake for 13-16 minutes or until no longer glossy. Cool before frosting.
To make frosting: beat butter and cream cheese with an electric mixer until smooth. Slowly mix in powdered sugar then add vanilla and salt. Beat on medium high speed until smooth.
Frost cookies as desired, top with a dusting of cinnamon or finely chopped nuts.
Store in an airtight container for up to 3 days or freeze (frosted or unfrosted) for up to 2 months.
