Preheat the oven to 350°F and line a baking sheet with parchment paper or baking mat. Set aside.
Using a stand-mixer with a paddle attachment or a hand mixer, beat the butter and sugars for about 2 minutes until light and fluffy. Add in the eggs one at a time and beat till combined. Add the vanilla and beat until combined.
In a separate medium bowl, mix the flour, baking powder, baking soda, cinnamon and salt together. Slowly mix the dry ingredients into the wet ingredients.
Scrape down the sides of the bowl. Gently stir in the carrots and raisins. Using a medium cookie scoop (you want them a little larger than a silver dollar), scoop the dough onto the prepared baking sheet, leaving about 1 ½ inches between each cookie. Bake for 10-12 minutes. The cookies should begin to brown on the edges. Remove from the oven and allow the cookies to cool.
Put the butter and cream cheese in the bowl of a stand mixer with a whisk attachment. Whip the butter and cream cheese until light and fluffy for about 3 minutes. Add the vanilla extract. Slowly add the powdered sugar and whip to combine. The frosting will be thick, but fluffy.
Transfer the frosting to a plastic bag and snip off the end. Pipe a thick layer of frosting on one cookie and place another one on top to sandwich together. Repeat with the remaining cookies.