In a large mixing bowl, mix together 1 cup of flour, sugar, baking powder, baking soda, salt, and nutmeg.
In small mixing bowl, whisk together buttermilk, butter, and eggs. Add wet ingredients to the dry and mix on medium speed for about 30 seconds.
With speed on low, gradually mix in the remaining flour a little at a time. Add more or less flour as necessary to make a soft dough that is moist and slightly tacky. Cover bowl with plastic wrap and chill for 1 hour.
Place oil in a Dutch oven and heat to 375°.
Prepare the glaze by whisking together the powdered sugar, vanilla and water until smooth. Add additional powdered sugar or water if necessary for a thin glaze.
On a lightly floured surface, use a floured rolling pin to roll out the dough to ½ inch thick. Use a floured donut cutter or a large and a small biscuit cutter to cut out the donuts and donut holes. Gather scraps together and roll out again to cut more donuts. Lightly score the donuts three times, making a triangle in the ring of the donut to help create the “petals”.
Cook several donuts at a time scored side up, flipping them over as they rise to the surface and turn golden brown, about a minute per side. Drain on a wire rack. Before frying another batch, make sure oil temperature has returned to 375 degrees and cut one open to make sure they are cooked through. The exteriors should be deep brown and light and not doughy.
Remove the donuts from the oil and set them on the rack to drain and cool slightly.
While still warm, dip the donuts, petals side down, into the glaze. Swirl the donut in the glaze a little, then pick it up and let the excess glaze dribble back into the bowl.
Return the glazed donut to the rack to let the glaze dry.
Repeat the process until all donuts and donut holes have been cooked and glazed.