For the doughnuts: Sift together the flour, baking powder, salt, baking soda and nutmeg in a large bowl. In the bowl of a stand mixer fitted with the paddle attachment, combine the granulated sugar, buttermilk, sour cream, melted butter, vanilla and eggs. Beat on medium speed until fluffy, about 2 minutes.
With the mixer on low, add the dry ingredients, mixing until just blended. It will be quite wet, so refrigerate for at least 30 minutes.
Heavily flour a work surface and your hands. Remove the dough from the bowl, place it on your work surface and pat the dough into 9 1/2-by-11-inch rectangle about 1/2-inch thick. Cut out doughnuts with a floured doughnut cutter to make 6 doughnuts and 6 doughnut holes. Pat out the dough scraps to make 3 more doughnuts and doughnut holes. Set aside on a tray.
Meanwhile, fill a large heavy pot with 2 inches of oil. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 350 degrees F. Fry the doughnuts and doughnut holes a few at a time until golden brown, 1 to 2 minutes. Gently flip and continue to fry until golden brown, 1 to 2 minutes more. When both sides are golden brown, carefully transfer the doughnuts to a cooling rack lined with paper towels. Continue until all the doughnuts are fried.
For the glaze: Combine the strawberries, water, vinegar and vanilla bean in a small pot over medium heat. Cook until juicy, about 10 minutes. Let cool slightly then blend until smooth. Pour into a bowl, add the confectioners' sugar and whisk thoroughly until light pink.
Move the doughnuts onto a cooling rack. Pour the glaze over the doughnuts and top with sprinkles. Let the doughnuts set for 5 minutes before enjoying.