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For the cake doughnuts: In the bowl of a stand mixer fitted with the paddle attachment, beat together the eggs and sugar until it becomes a pale yellow color, approximately 15 minutes. Add the vanilla and mix to combine. In a separate bowl combine the flour, baking powder, nutmeg and salt. Stir together the milk and the butter.
Alternate adding the flour mixture and the milk mixture to the egg mixture and mix on low speed until it forms a smooth dough that is somewhat sticky, about 5 minutes. Place the dough in a lightly-oiled bowl, cover with plastic wrap or a tea towel and let rest at room temperature, 1 hour.
Preheat 5 inches oil in a conventional fryer or a medium pot to 365 degrees F. Roll out the dough on a floured surface and cut out doughnuts. Place several in the oil and fry until lightly browned, 2 minutes on each side. Transfer to a paper towel to absorb excess grease. Let cool completely, 1 hour.
For the panko and toasted almond topping: Meanwhile, heat the sesame seeds in a small dry pan over low heat, continuously stirring, until they pop and begin to show signs of browning. Remove from the heat and mix into the panko.
Dip 1 side of each doughnut in the glaze, then the panko-sesame seed mixture.