Prep: preheat the oven to 350 F. Grease and flour a non-stick standard size loaf pan (4.5 inches x 8.5 inches or 9x5 inches).
Brown the butter: set the butter in a light colored frying pan over medium heat. Cook as the butter melts and begins to sputter. Small panko-like bits will fall to the bottom, keep cooking and stirring while those bits turn brown. The butter will smell nutty and it will stop sputtering, going silent as all of the water has evaporated and the milk solids have turned brown. Immediately transfer to a large bowl, where you’ll make the pumpkin cake batter.
Split the butter: remove 1 tablespoons of brown butter, mostly brown butter bits, from the big bowl and add it to a small to medium sized bowl. The smaller bowl will be for the glaze. You’ll have around 160g browned butter in the larger bowl.
Bloom the spices: to the hot brown butter for the pumpkin batter, add the pumpkin spice (2 tablespoons) and stir. The heat brings out their flavor. Add the salt (½ teaspoon) and vanilla (1-2 teaspoons), let cool.
Make the pumpkin spice sugar swirl: whisk together the fine granulated sugar (5 tablespoons) and pumpkin spice (1 tablespoons). Set aside.
Make the batter: add the sugar (200g or 1 cup brown sugar50g or ¼ cup fine granulated sugar) to the bowl then whisk, very well until the sugar and butter are no longer separated. Add the two eggs, one by one and whisk very well - at least 2 minutes. Whisk in the can of pumpkin puree then add the flour (275g or 2 cups plus 2 tablespoons), baking soda (½ teaspoons) and baking powder (1 ½ teaspoon). Whisk until the mix is smooth.
Layer the batter into the pan: dollop a third of the pumpkin batter into the pan, smooth it into an even layer. Sprinkle half of the sugar mixture on top, covering all of the pumpkin batter. Spread another third of pumpkin batter over the sugar, then sprinkle the rest of the pumpkin spice sugar over the top - covering all of the pumpkin batter. Add the remaining pumpkin batter on top and smooth into an even layer. It will come close to the rim of the pan but this isn't a high rising bread so it'll be fine.
Bake the pumpkin bread: until a cake tester comes out clean, for about 50-60 minutes. Let cool briefly in the pan then transfer to a wire rack to fully cool.
Make the glaze: into the bowl with the 1 tablespoon of reserved brown butter, add the powdered sugar (130g or 1 cup), vanilla bean paste (1 teaspoon), a pinch of salt and 2-3 tablespoons of milk (heavy cream works too). Whisk until smooth. Spoon the glaze over the cooled pumpkin bread. The bread will keep for 3-4 days though it’s best not to cover the glazed part (it will act as a barrier anyway). I wrap the bottom in foil and leave the glazed top exposed.