Dissolve yeast in water:

Place the lukewarm water in a small bowl, sprinkle the yeast over it, and whisk until fully dissolved. Reserve.

Combine milk with yeast:

Heat the milk until scalded, then allow it to return to lukewarm. Combine the lukewarm milk with the yeast mixture.

Mix egg mixture:

In another bowl, mix the eggs, margarine, sugar, salt, and nutmeg until uniform. Incorporate this into the milk-yeast blend.

Knead dough:

Slowly incorporate the bread flour, kneading until the dough becomes smooth and pliable.

Proof dough until doubled:

Set the dough in a warm area, cover with waxed paper, and allow to proof until doubled, roughly 2 hours.

Shape into ovals:

Deflate the dough, split into two equal portions. Roll each to a 3/4-inch (2 cm) thickness, then slice into 7-inch-long (18 cm) ovals.

Proof again:

Let the cut pieces proof once more until they become light and airy.

Fry until golden:

In a deep pan, heat vegetable shortening to a depth of 2 to 3 inches (5-7.5 cm) until very hot (approximately 350°F (175°C)/177°C). Fry the pieces in batches till golden, roughly 2 minutes per side. Transfer to paper towels to drain and cool.

Make vanilla frosting:

For the frosting: In a medium bowl, beat the butter with the vanilla and 1 cup (120 g) of the powdered sugar until creamy. Slowly add the milk and remaining powdered sugar, stirring until the mixture is smooth.

Frost cooled rolls:

Once the rolls have cooled completely, apply the frosting if desired.