Position a rack in the center of the oven and preheat it to 375F. Line the bottom and sides of a 9 by 5-inch loaf pan with parchment paper.

Set a small saucepan over medium heat and add the butter. Melt the butter, then let it foam and cook, stirring occasionally until flecks of brown form at the bottom of the pan, 4 to 6 minutes. Transfer the brown butter to a medium bowl and whisk to let it cool.

Whisk ¾ cup of the sugar into the brown butter. Crack in the eggs and add the vanilla. Whisk vigorously into a smooth mixture. Add the squash directly into the bowl (there might still be chunks, but that's fine) and whisk to combine. Switch to a spatula and fold in the flour, baking powder, ½ teaspoon of the cinnamon, the allspice, and 1 teaspoon salt. Stir to combine into a nice, thick batter.

Scrape the batter into the lined loaf pan and bake until a toothpick inserted comes out clean, 50 to 55 minutes. Let cool for 10 minutes before removing the cake from the pan onto a wire rack. Continue to let cool for at least another 30 minutes before serving.

While the cake is baking, in a stand mixer fitted with the whisk attachment or with a hand mixer, combine the heavy cream, the remaining ½ teaspoon cinnamon, and the remaining 1 tablespoon sugar and beat on medium-high speed until stiff peaks form, 2 to 3 minutes. Chill the cream in the fridge until the cake is ready.

To serve, slice the cake and serve with the cinnamon whipped cream.