Preheat your oven to 350 F. Prep a sheet pan by placing parchment paper on top of the sheet pan. Set aside.
In a stand size mixer, fitted with the paddle attachment, cream the butter, brown sugar, and granulated sugar on medium high speed until smooth and creamy. About 3 minutes.
On a medium-low speed, add in the shredded carrots, vanilla extract, and whole egg and mix until smooth. This should take about 30-45 seconds.
With the mixer on the lowest speed, add in the flour, baking powder, cinnamon, nutmeg, ginger, cloves, salt, and mix just until the flour mixture disappears.
With a kitchen scale or a large cookie scoop, weigh out 4 ounces balls, or scoop out 6 equal cookie balls. Place them on the prepared baking sheet. Place the sheet pan in the fridge while you make the crumb topping.
To make the topping: In a medium-size bowl, using your hands, mix all the ingredients until they are combined and have a “shaggy” look. There should be no flour streaks.
Once the crumb topping is done, coat the top of the cookies with the crumb until they are completely covered.
Bake for 14-16 minutes, while they are baking make the cream cheese drizzle.
For the cream cheese glaze
In a small microwaveable bowl, melt the butter.
In a stand sized mixer fitted with the paddle attachment, beat the cream cheese for 30 seconds. Scrape down the sides, and add the butter and continue beating. Add powdered sugar, vanilla, and salt. Beat until combined.
Once the cookies are cool, drizzle with the cream cheese glaze and serve.