Process the oats in a food processor by pulsing 3-5 times. The oats should still have pieces that are approximately ½ the size of original oats (not fully ground); set aside.
1 cup old-fashioned oats
Grate the carrots and place the grated carrots on 3-4 layers of paper towels. Top the carrots with more paper towels and tightly roll up the carrots, squeezing as you roll to remove as much moisture as possible; set aside.
3 cups grated carrots
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, coconut oil, brown sugar, and granulated sugar together until light and fluffy, about 3 minutes at medium speed.
½ cup unsalted butter, ½ cup coconut oil, 1 cup brown sugar, ¾ cup granulated sugar
Add the salt and vanilla and beat another 2 minutes at medium speed until fully incorporated, smooth, and fluffy.
2 teaspoons kosher salt, 1½ teaspoons pure vanilla extract
On medium-low speed, add the eggs, one at a time, scraping down the bowl after adding each egg. Mix just until fully incorporated, about 30 seconds per egg.
2 large eggs
In a large bowl, sift the all-purpose flour, bread flour, baking soda, baking powder, cinnamon, apple pie spice, and ground ginger together. Add the flour mixture to the wet ingredients in one addition and mix on low speed until the flour is incorporated and no dry flour can be seen. (Don’t mix too long or too much gluten will form, making the cookies a little tough.)
1¾ cup all-purpose flour, ½ cup bread flour, 1 teaspoon baking soda, 1 teaspoon baking powder, 1½ teaspoons ground cinnamon, 1½ teaspoons apple pie spice, 1 teaspoon ground ginger
Add the oats, coconut, grated carrots, raisins, and pecans and mix on the lowest speed just until incorporated.
¾ cup sweetened shredded coconut, ¾ cup golden raisins, ¾ cup chopped roasted pecans
Cover the dough and refrigerate for 30 minutes before scooping and baking.
While the dough rests in the refrigerator, adjust the oven rack to the middle position, heat the oven to 350°F, and line 2 baking sheets with parchment.
When ready to bake, scoop cookie dough using a #40 scoop (a 2-tablespoon scoop) and place scoops of cookie dough 2 inches apart onto the lined cookie sheets.
Bake 12-15 minutes, rotating the cookie sheet halfway through baking. The cookies should be slightly darker in color with slightly firm edges and centers still slightly soft to the touch.
Let the cookies cool for 1 minute on the baking sheet, then use a spatula to transfer the cookies to a wire rack to completely cool.
While the cookies cool, make the frosting: In the bowl of a stand mixer fitted with the paddle attachment, cream the powdered sugar, cream cheese, and butter together for 3 minutes on medium speed, or until light and fluffy.
1¼ cup powdered sugar, 8 ounces cream cheese, 5 tablespoons unsalted butter
Add sour cream, vanilla extract, ground ginger, salt, lemon juice and zest, and orange juice. Beat on medium speed until smooth and fully incorporated, about 1 minute.
2 tablespoons sour cream, ½ teaspoon pure vanilla extract, ¼ teaspoon ground ginger, ½ lemon, ½ orange, ½ teaspoon kosher salt
The frosting can be used immediately. If making ahead, the frosting will keep refrigerated in an airtight container for up to 3 days. When ready to use, let the filling come to room temperature and fluff it up using an electric mixer with a paddle attachment at medium speed for 1 minute before using.
To assemble the cookies, spread about 1½ tablespoons of the cream cheese filling onto the flat side of 24 cookies and top with a second cookie (flat sides together). Slightly press the sandwich cookie together so both sides stick together.