In a large bowl, whisk together the flour, baking powder, salt, and sugar.

In another bowl, beat the egg, milk, melted butter, and vanilla extract together until mixed.

Combine the wet and dry ingredients. Stir gently until they are just mixed.

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

Drop teaspoonfuls of batter into the hot oil. Fry until golden brown, about 2 minutes per side.

Drain them on paper towels.

Heat the heavy cream, sugar, vanilla, and cornstarch in a saucepan over medium heat.

Stir continuously until it thickens. Remove it from heat and let it cool.

Fill a pastry bag with the vanilla cream. Once the doughnut holes are cool, inject each with cream using a small nozzle.

Melt the chocolate chips and heavy cream together in the microwave or over a double boiler until smooth.

Dip the top of each filled doughnut hole into the chocolate glaze. Allow the glaze to set before serving.