Preheat the oven to 350 degrees F. Spray an 8 1/2-by-4 1/2-inch loaf pan with the baking spray then line it with parchment.
Place the butter in a small saucepan and cook over medium-high heat, stirring occasionally, until deep golden, 3 to 5 minutes. Immediately pour it into a heatproof liquid measuring cup. Add the oil to the brown butter; set aside.
Combine the carrots, coconut and nuts in a small bowl and toss to combine; set aside.
Whisk together the flour, baking powder, cinnamon, salt, ginger and baking soda in a small bowl; set aside.
Combine the granulated and brown sugars, eggs and vanilla in the bowl of a stand mixer fitted with the whisk attachment. Mix on the highest speed for 1 minute. Reduce the speed to medium and slowly pour in the butter and oil. Increase the speed to high and beat until the mixture lightens in color and resembles the consistency of mayonnaise, about 1 minute..
Add the dry ingredients then mix on low speed just until combined. Scrape the bowl and whisk attachment with a rubber spatula.
Remove the bowl from the stand mixer and fold in the carrot mixture with a rubber spatula until combined. The batter will be thick. Spoon the batter into the prepared pan and smooth the top.
Bake until a toothpick inserted in the center of the loaf comes out with a few moist crumbs, 58 to 62 minutes. Let cool completely in the pan then remove from the pan and serve.
The flavor and texture of this bread intensifies and improves after sitting overnight.