Place the butter and brown sugar in a large mixer bowl and beat until smooth and creamy, about three minutes. Add the eggs, carrot puree, and vanilla, one at a time, beating well after each addition. Scrape down the sides of the bowl. Place the flour, cinnamon, baking powder, baking soda, and salt in a separate bowl, mix well, and with the mixer on low, add to the butter mixture. Beat just to combine. Stir on oats, carrots, and almonds and mix to combine.
Place the butter and sugar in a large mixer bowl and beat until smooth and creamy, about three minutes. Add the lime juice, lime zest, and vanilla, beating to combine. Scrape down the sides of the bowl and beat again. With the mixer on low, add flour and beat, scraping again, until combined. Stir in almonds and mix until well combined.