Brown butter in a saucepan until golden and nutty. Cool slightly.
Preheat oven to 350°F (175°C). Grease a loaf pan with browned butter.
In a large bowl, combine pumpkin purée, sugars, eggs, milk, browned butter, oil, vanilla, and salt. Mix smooth.
Sift in flour, baking soda, and pumpkin spice. Stir gently to combine.
Pour batter into pan and bake 40–45 minutes, until a toothpick comes out with moist crumbs.
Cool loaf 15 minutes in pan, then transfer to rack.
For glaze: whisk browned butter, maple syrup, powdered sugar, and a splash of milk. Add salt and vanilla if desired.
Drizzle glaze over cooled bread. Slice and serve.