Preheat oven to 350°F (175°C) and prepare a 9 × 5-inch loaf pan with parchment paper.
Brown the butter over medium heat until the milk solids become golden brown and smell nutty. Transfer immediately to a bowl and cool for about 10 minutes.
Whisk flour, baking soda, baking powder, salt, cinnamon, ginger, nutmeg, and cloves together.
In another bowl, whisk pumpkin, both sugars, eggs, oil, and vanilla.
Whisk in the slightly cooled browned butter, including the browned milk solids.
Fold the dry ingredients into the wet mixture just until combined.
Transfer the batter to the prepared loaf pan.
Bake for 55–65 minutes, or until a tester inserted near the center comes out clean or with moist crumbs.
Cool for 15 minutes in the pan, then transfer to a wire rack and cool completely.
Whisk together the glaze ingredients, adding milk gradually until thick but pourable.
Drizzle over the completely cooled loaf.
Allow the glaze to set for 15–20 minutes before slicing.