Turn on the oven to 300 degrees. Spray a standard-size (not jumbo) 12-cup muffin tin with non-stick spray and line each cup with a paper cupcake liner.
Scoop the butternut pieces into a microwave-safe bowl, cover with plastic wrap, poke a few holes in the top, and microwave on high for 10 minutes. Uncover the bowl and mash with the back of a large spoon until it’s the consistency of loose mashed potatoes. Let cool completely.
In a small bowl, mix the brown sugar with ¼ cup of the pecans and set aside. Stir the sour cream and vanilla into the now-cool butternut, then whisk in the eggs, one at a time, until the mixture is smooth (though if you have a few lumps you can’t get rid of, that’s okay).
Pour the flour, granulated sugar, cinnamon, baking soda, baking powder and salt into the bowl of a stand mixer fitted with the paddle attachment—or, if you’re using a hand mixer, into a large bowl—and mix on low speed for 30 seconds. Add the butter and mix until well blended, about 1 minute. Stop the mixer, add half of the squash mixture and beat on medium speed for 30 seconds. Stop the mixer, scrape down the sides of the bowl with a spatula, add the rest of the squash and beat on medium until you have a smooth batter, about 30 seconds more. Add the remaining ½ cup of the pecans and mix until just incorporated.
Divide the batter among the muffin cups (you’ll use about 3 tablespoons per muffin) and top each with a rounded teaspoon of the brown sugar mixture. Bake, rotating the pan halfway through, for about 25 minutes, until the muffins spring back when gently pressed and a skewer inserted into their middle comes out almost clean (a few crumbs attached is fine). Cool in the pan on a cooling rack for 20 minutes before unmolding.