Dissolve yeast in the warm water in the bowl of your stand mixer.

Add milk, rum, sugar, salt, Lebkuchen spice*, eggs, butter, vanilla, and 2 cups flour.

Beat on low for 30 seconds with the paddle attachment, scraping the bowl if needed.

Beat on medium speed for 2 minutes, scraping bowl occasionally.

Stir in remaining flour until smooth.

Cover and let rise until doubled, about an hour.

Turn dough onto floured surface and roll dough 1/2-inch thick.

Cut with a floured doughnut cutter (I used a star cutter and then a small identical star cutter to create the hole in the centers).

Place the cutouts on the parchment lined baking sheet.

Cover and let rise again until doubled in size, 30-40 minutes.

Heat vegetable oil in deep fryer to 350 degrees F and fry until golden brown, about 30 seconds on each side.

Remove from the oil and drain on paper towels for a minute.

Set them on cooling racks over the parchment lined baking sheets. Make sure the parchment is clean and free from crumbs.

Whisk in the powdered sugar and Lebkuchen spice until combined.

If the glaze is too thick to dip the doughnuts into, thin it out by adding more milk one teaspoon at a time.

Dip the doughnuts into the glaze and set them on cooling racks over parchment or foil-lined baking sheets. Sprinkle with the edible decorations.

If you run out of glaze, scrape up the excess off of the parchment paper on the baking sheet and return it to the bowl.

Let the glaze harden completely before serving.