Brown the butter: Melt the butter in a light-colored saucepan over medium heat. Let it foam, then quiet down, then turn amber with toasted specks on the bottom, about 5 minutes. Pour into a large mixing bowl to cool slightly.

Blot the pumpkin puree: While the butter cools, spread the pumpkin puree on paper towels and press firmly with more paper towels. Repeat until the towels stop coming away wet; this keeps the batter from turning gummy.

Preheat and prep the pan: Preheat the oven to 350°F. Grease an 8x8-inch baking pan or line it with parchment paper, leaving an overhang for easy removal.

Whisk the wet ingredients: Add the brown sugar, blotted pumpkin, egg and vanilla to the browned butter. Whisk until smooth and glossy, about 1 minute.

Mix the dry ingredients: In a separate bowl, whisk together the flour, pumpkin pie spice, baking powder and salt until evenly combined.

Combine wet and dry: Fold the dry ingredients into the wet mixture just until no dry streaks remain. Do not overmix, or the bars will turn tough instead of chewy.

Fold in the chips: Stir in the white chocolate chips, saving a small handful to scatter on top of the batter for a bakery-style look.

Spread the batter: Transfer the thick batter to the prepared pan and spread it evenly with a spatula, pushing it into the corners.

Bake the bars: Bake for 25 to 28 minutes, until the edges turn golden and pull slightly away from the pan sides. A toothpick inserted near the center should come out with a few moist crumbs.

Cool completely: Let the pan cool on a wire rack for at least 1 hour. Cutting too early causes the bars to crumble instead of slicing cleanly.

Make the cinnamon glaze: Whisk together the powdered sugar, milk and cinnamon until smooth and pourable, adding more milk a few drops at a time if needed.

Glaze and slice: Drizzle the glaze over the cooled bars, then lift them out using the parchment overhang. Slice into 16 squares with a sharp knife.