Preparation of the Orange Cream Cheese Filling:

1. Step 1: Combination: In a medium mixing bowl, combine the cream cheese, powdered sugar, vanilla extract, and orange zest. Using an electric mixer, beat the mixture until it is smooth and creamy.
2. Step 2: Refrigeration: Transfer the filling to the refrigerator to chill until required for stuffing the cookies.

Roasting the Carrots:

1. Step 1: Preheating: Preheat the oven to 375 degrees Fahrenheit (190 degrees Celsius).
2. Step 2: Arrangement: Place the finely grated carrots in a single layer on a baking sheet lined with parchment paper, spreading them out as evenly as possible.
3. Step 3: Initial Roasting: Roast in the preheated oven for 10 minutes, then stir the carrots to ensure even cooking.
4. Step 4: Final Roasting: Continue to roast for an additional 10 minutes, or until the carrots are fragrant and lightly browned.
5. Step 5: Cooling: Remove from oven and allow the carrots to cool on the baking sheet.

Preparation of Carrot Cake Cookies:

1. Step 1: Butter Mixture: In a large bowl, combine the cooled brown butter with granulated sugar, brown sugar, and salt. Stir until well mixed.
2. Step 2: Incorporation of Wet Ingredients: Add the egg, vanilla extract, and spices to the butter mixture. Mix thoroughly until the mixture is smooth and glossy, ensuring no traces of egg remain.
3. Step 3: Dough Formation: Sift together the flour and baking soda. Gradually add these dry ingredients to the wet mixture, mixing until a soft dough forms.
4. Step 4: Addition of Carrots and Other Ingredients: Once the carrots have cooled, fold them into the dough along with the instant oats, chopped pecans, and shredded coconut.
5. Step 5: Portioning: Using a 3-ounce cookie scoop or a tablespoon, scoop eight portions of dough.
6. Step 6: Stuffing the Cookies: Remove the orange cream cheese filling from the refrigerator. Flatten each portion of dough into a disc. Place a teaspoon of filling in the center of each disc, then enclose the filling by pinching the dough shut.
7. Step 7: Chilling: Place the stuffed dough portions on a cookie sheet and refrigerate for at least one hour, or overnight if possible, to firm up.
8. Step 8: Baking: Preheat the oven to 325 degrees Fahrenheit (163 degrees Celsius). Arrange cookies on a parchment-lined baking sheet, spacing them well apart. Bake for 14-16 minutes, or until the cookies are slightly domed and the edges have turned golden brown.
9. Step 9: Cooling: Allow the cookies to cool on the baking sheet for at least one hour to set properly before serving.