In the bowl of a stand mixer, sift together the flour, salt, nutmeg and ⅓ cup sugar. Set aside.
In a small bowl, combine the 1 teaspoon of sugar with the active yeast and warm water. Allow to sit for 5 minutes until it becomes foamy.
In a medium sized bowl add the cubed butter and pour the warm milk over it. Allow the butter to melt and for the mixture to come to room temperature.
In a separate bowl, whisk the eggs together.
Add the yeast mixture, butter mixture and eggs to the flour mixture. Attach the dough hook and knead on low-medium speed for 10 minutes. The dough is ready when it starts to pull away from the sides of the bowl and feels soft (not overly sticky) to the touch.
Meanwhile, grease a large bowl with a drop of oil.
When the dough is ready, transfer it to the greased bowl and cover with cling film. Allow it to rise in a warm space for one hour, until roughly doubled in size.
Once the dough has risen, punch it back to deflate it a little, and transfer to a floured surface.
Roll the dough out to 1½ inches thick , and use a heart shaped cookie-cutter to cut out each doughnut.
Place on a lined baking sheet, cover with cling film and allow to rise again for another 20 - 25 minutes.
When the dough is ready, heat oil in a heavy bottomed pan or dutch oven until it reaches between 340 and 350°F. Any hotter than this and the doughnuts will brown on the outside but be raw inside.
Fry 2 - 3 doughnuts at a time until golden brown, then flip over to the other side. Usually 1 - 2 minutes per side is good.
Place the fried doughnuts on a wire rack and allow to cool fully.
Once cooled, use a piping big filled with jam and a long narrow tip. Insert the tip into the doughnut and fill with jam. Then lightly roll the doughnuts in granulated sugar. If the sugar is not sticking, use your finger to lightly sprinkle some water on the doughnut prior to rolling in the sugar.