1 1/2 cups confectioners sugar, plus more if needed
1 teaspoon vanilla extract
Preheat your oven to 350° F, and grease two 9-inch loaf pans.
In a large frying pan, heat the butter over medium high heat. It will melt first, and then start to foam. Turn the heat down to medium. Stir the melted butter almost constantly, scraping any browning bits from the bottom of the pan. When the butter has turned a brown color and smells rich and nutty, remove it from the heat. (This should take about 7 minutes). Allow it to cool for about 10 minutes.
In the bowl of a standing mixer, beat together the eggs and sugars on high speed for several minutes, until the color has lightened (Random side note: in Norwegian this is called an “eggedosis”). Scrape in the browned butter and beat for another couple of minutes, until the mixture is smooth.
Add the puréed squash to the wet ingredients and beat until smooth and uniformly mixed in.
In a small bowl, combine the flour, salt, baking powder, baking soda, and nutmeg. Add this to the wet ingredients, and mix on low until fully incorporated.
Divide the batter evenly into the 2 prepared loaf pans and bake for about 50 minutes, until a tester comes out clean. Take the bread out of the loaf pans and allow to cool completely before glazing (recipe below).
For the brown butter icing.
Brown the butter in a pan, just as described in step 2 for the bread (it may take a little less time because there’s less butter) and allow to cool for about 10 minutes. Scrape the butter into a mixing bowl.
Sift the confectioner’s sugar to remove lumps. Then whisk the vanilla into the butter. Next, whisk in confectioner’s sugar until your reach a spreadable consistency.
Spread the icing onto the loaves, and allow to set for about 30 minutes before slicing.