Place a rack in the upper third of the oven and preheat oven to 350 degrees F. Lightly grease (or spray with nonstick baking spray) a half sheet pan (18×13-inch).
In a large bowl whisk together flour, granulated sugar, cornstarch, baking soda, spices, and salt.
Place a medium saucepan over medium heat to melt and brown butter. Allow the butter to melt and crackle as the water cooks out. Once the crackling subsides, keep an eye on the butter as the solids will start to brown. Just as the butter begins to brown, remove the pan from the heat and whisk in the milk powder. The butter will foam and froth and make a fuss. Just keep whisking until well browned (in all honestly – it’ll be hard to see the browning for all the foam – that’s fine. It’ll be delicious). After whisking the milk powder to smooth and toasty (about 30 seconds) pour into a medium bowl. Add the pumpkin puree and very carefully whisk. The pumpkin will seize and that’s okay.
Add the buttery pumpkin mix to the dry ingredients and use a rubber spatula to fold a few turns. Add the eggs, vanilla extract, and sour cream, and fold until well-combined and no hidden flour pockets remain.
Spoon batter into the prepared pan and use an offset spatula to spread the batter into an even layer from edge to edge. Bake for 18-22 minutes, rotating once during baking, until golden around the edges and firm but bouncy.
While the cake bakes, make the frosting. In a medium saucepan (you can use the first saucepan you melted butter in, just give it a rinse!), again melt and brown the butter. Remove from the heat and whisk in corn syrup, milk, vanilla extract, and salt. Whisk in the powdered sugar until smooth, followed by the pecans.
Quickly pour the warm frosting over the warm cake and use the offset spatula to spread it from edge to edge. You’ll need every bit of frosting so scrape the pan well. Allow the cake to set and cool for an hour before serving.
