Heat your oven to 350 degrees F. Line 12 baking cups with paper liners or lightly coat with nonstick spray. Set aside. If using nuts for the mix-ins, toast them in the oven now: Spread the nuts into an even layer on an ungreased baking sheet. Bake at 350 degrees F for 8 to 12 minutes (for pecan or walnut halves), until they are lightly browned and fragrant. Transfer the nuts immediately to a cutting board; roughly chop and set aside.

Place the coconut oil in a medium microwave-safe bowl. Heat in the microwave just until melted (about 30 seconds on high). Set aside to cool to room temperature.

In a large mixing bowl, whisk together the flour, oats, baking powder, baking soda, cinnamon, ginger, and salt. Add the grated carrot and apple and fold to combine.

To the bowl with the coconut oil, add the eggs, Greek yogurt, honey, and vanilla. Whisk until smooth. If the coconut oil resolidifies, warm it in the microwave in 15-second bursts, and stop as soon as you can stir the mixture back together. Add the wet ingredients to the dry ingredients, and stir gently until just combined. Do not overmix. Fold in the nuts or any other mix-ins.

Divide the batter evenly among the 12 muffin cups. Bake for 18 to 22 minutes, or until a toothpick inserted in the center of a muffin comes out clean.  Place the pan on a wire rack and let the muffins cool in the pan for 4 minutes. Gently transfer the muffins to the rack to finish cooling completely.

For the icing: Whisk together the powdered sugar, honey, and 1 teaspoon milk. Continue to add milk, 1 teaspoon at a time, until your desired consistency is reached. Drizzle over the top of the cooled muffins.