In a mixing bowl, combine warm milk and yeast. Let it sit for 5 minutes until frothy.

Add flour, sugar, salt, egg, and melted butter to the yeast mixture. Mix until a dough forms.

Knead the dough on a floured surface for about 5-7 minutes until smooth.

Place the dough in a greased bowl, cover, and let it rise in a warm place for 1 hour or until doubled in size.

In a mixing bowl, whip the heavy cream until soft peaks form.

Gently fold in matcha powder, powdered sugar, and vanilla extract until well combined.

Transfer the filling to a piping bag and refrigerate until ready to use.

Once the dough has risen, punch it down and roll it out to about 1/2 inch thickness.

Cut out donuts using a donut cutter or two round cutters.

Heat oil in a frying pan to 350°F (175°C). Fry the donuts in batches until golden brown, about 2-3 minutes per side.

Remove donuts and place them on a cooling rack to drain excess oil.

Once the donuts are cool, use the piping bag to fill each donut with the matcha filling.

Serve immediately or store in an airtight container.