In a large bowl, beat the butter, brown sugar and granulated sugar with a mixer on medium speed for 2 minutes, until light and fluffy. Beat in the milk and vanilla until combined.
In a separate bowl, whisk together the flour, oats, cinnamon, ginger, nutmeg, baking soda and salt. Add to the butter mixture and mix on low just until combined.Fold in the grated carrots, walnuts and raisins. Use the small holes of a box grater for the carrots so they melt into the cookies.
Cover and chill the dough for 30 minutes. Near the end, preheat the oven to 350°F and line two baking sheets with parchment paper.
Scoop the dough into 1 1/2 tbsp mounds, place them 2 inches apart and flatten each one slightly to about 1/2 inch thick, since they don't spread much.
Bake for 11-13 minutes, until the edges are lightly golden and the centers are set but still soft. Cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.
In a medium bowl, beat the cream cheese and butter until smooth. Add the powdered sugar, vanilla and salt and beat until light and fluffy.
Spread or pipe about 1 tbsp of frosting onto the flat side of half the cookies and top with the remaining cookies. Store leftovers in an airtight container in the fridge for up to 4 days. Makes about 12 sandwich cookies.