Dissolve the yeast and a teaspoon of sugar in warm milk. Let it sit for 10 minutes until frothy.

In a large bowl, combine flour, sugar, and salt.

Add the yeast mixture, eggs, melted butter, and vanilla extract.

Mix until a dough forms, then knead for about 8-10 minutes until smooth.

Place the dough in a greased bowl, cover, and let rise for 1-2 hours until doubled.

If using homemade lemon curd:

Whisk together 4 egg yolks, ½ cup sugar, ½ cup lemon juice, and 1 tablespoon lemon zest in a saucepan.

Cook over medium heat, stirring constantly until thickened.

Remove from heat and stir in 4 tablespoons of unsalted butter. Let it cool completely.

Roll the dough on a lightly floured surface to about ½-inch thickness.

Cut out rounds using a doughnut cutter.

Heat oil in a deep fryer or pot to 350°F (175°C).

Fry the doughnuts in batches for about 1-2 minutes per side until golden brown.

Remove and drain on a paper towel-lined plate.

Once cooled, fill a piping bag with lemon curd.

Make a small hole in each doughnut and pipe the lemon filling inside.

Roll the doughnuts in sugar mixed with lemon zest.