Preheat the oven to 425F. Line a 12-cup muffin pan with paper liners.
Melt the butter in a small saucepan over medium-low heat and then let it cool to room temperature. If the butter starts to splatter, reduce the heat to low.
Place the all-purpose flour, salt, baking powder, and baking soda in a medium bowl and whisk for 20 seconds to thoroughly combine all the ingredients.
Place the brown sugar, cinnamon, and nutmeg in a bowl and whisk together. Whisk in the melted butter, then add the eggs one at a time and whisk until each egg is thoroughly incorporated. Whisk in the sweet potato puree and sour cream.
Let the wet ingredients sit for 10 minutes to give time for the sugar to dissolve.
Add half of the flour mixture to the wet ingredients. Use a spatula to fold the dry ingredients into the wet ingredients. Add the remaining flour mixture and fold it in until the dry ingredients are thoroughly incorporated, and no white specs of flour remain. The batter may be a little lumpy which is okay.
Divide the batter between the 12 muffin cups. The batter should almost be the top of each paper liner. You will need to thoroughly scrape the bowl to completely fill the muffin cups. Top each muffin with the pecan streusel and lightly press the streusel into the batter.
Bake the muffins at 425F for 5 minutes, then without opening the oven door reduce the temperature to 350F and bake the cupcakes until the center is done and the temperature in the center of the muffin registers at 202F, about 15-18 more minutes.
Remove the muffins from the oven and let the muffins cool in the muffin pan for 5 minutes. Place the individual muffins on a wire rack to finish cooling. The muffins can be served warm.