In a medium saucepan, melt the butter over medium-low heat. As the butter melts, it’ll start to foam, then turn a clear golden color. Continue to stir the butter, scraping up any browned specks from the bottom of the pan as it starts to brown. It should have a nutty aroma.
Once browned and nutty, turn off the heat and pour the browned butter into a shallow bowl, allowing it to cool for at least 5 minutes.
In a large bowl, whisk together the flour, baking powder, baking soda, spices, and salt until combined; set aside.
In another bowl, whisk both sugars and the eggs together until thickened and combined, about 45 seconds. Whisk in the browned butter and oil. Add the yogurt and vanilla, and continue whisking until combined.
Using a rubber spatula, gently fold the wet ingredients into the dry ingredients until almost combined. Gently fold in the shredded carrots and chopped pecans. Batter should still be lumpy with a few spots of flour. Allow batter to rest for 1 hour at room temperature.