Preheat the oven to 350°F. Grease a 9x5-inch metal loaf pan and line it with parchment paper, leaving an overhang on the long sides for easy removal.
Add the butter to a light-colored saucepan over medium heat. Cook, stirring frequently, until the butter melts, foams, and develops golden-brown milk solids with a rich, nutty aroma, about 5–7 minutes. Immediately transfer to a heatproof bowl. Reserve 2 tablespoons of the browned butter for the glaze and allow the remaining butter to cool for approximately 10 minutes.
In a medium mixing bowl, whisk together the flour, cornstarch, baking powder, baking soda, salt, cinnamon, and nutmeg until evenly combined. Set aside.
In a large mixing bowl, whisk together the granulated sugar, brown sugar, and eggs for 30–60 seconds until smooth and slightly lightened. Add the pumpkin puree, Greek yogurt, whole milk, vanilla extract, and remaining cooled browned butter. Whisk until completely combined.
Add the dry ingredients to the wet ingredients. Using a rubber spatula, gently fold until no visible streaks of flour remain. Avoid overmixing. The batter should be thick, smooth, and spoonable.
Transfer the batter to the prepared loaf pan and smooth the surface. The batter should fill no more than approximately ¾ of the pan.
Bake for approximately 65–80 minutes, checking for doneness beginning at 60 minutes. If the top begins browning too quickly, loosely tent the loaf with aluminum foil. The bread is done when a toothpick inserted into the center comes out with a few moist crumbs but no wet batter. The internal temperature should be approximately 200–205°F.
Allow the pumpkin bread to cool in the pan for 15–20 minutes. Carefully lift it out using the parchment paper and transfer to a wire cooling rack. Let cool completely before glazing.
In a medium bowl, whisk together the powdered sugar, reserved browned butter, maple syrup, bourbon, vanilla extract, and a pinch of salt. Add whole milk 1 teaspoon at a time until the glaze is thick but pourable.
Pour the maple bourbon glaze generously over the cooled pumpkin bread, allowing it to drip naturally down the sides. Let the glaze set for approximately 15–20 minutes before slicing.