In a large mixing bowl, combine 1/2 cup of warm milk with 2 teaspoons of active dry yeast and 1 tablespoon of sugar. Let this sit for about 5 minutes, or until frothy. Then add ingredients for the dough and mix until a sticky dough forms, knead for 8-10 minutes until smooth.

Transfer the kneaded dough into a greased bowl, cover with a towel, and let it rise for 1 hour until doubled in size.

Prepare the matcha pastry cream by heating 2 cups of milk, then whisking egg yolks with sugar, matcha powder, and cornstarch. Gradually whisk hot milk into the egg mixture, then cook until thickened. Stir in vanilla extract.

After dough rises, gently punch it down, roll it out, and cut into donut shapes. Let them rise for another 30 minutes.

Heat vegetable oil to 350°F and fry the donuts in batches until golden brown. Drain on paper towels.

Once cool, fill each donut with matcha cream using a piping bag and dust with powdered sugar.