In a large mixing bowl, whisk together the all-purpose flour, sugar, fresh yeast, and salt. In a separate bowl, combine the warm milk, melted butter, and egg until blended.

Pour the wet mixture into the dry ingredients, stirring until a sticky dough forms.

Lightly oil a clean bowl, then place the dough inside and cover it with plastic wrap or a damp cloth. Set it in a warm area to rise for 1 to 1.5 hours.

Punch the dough down to release the air and turn it onto a floured surface. Roll it out to about a 1/2-inch thickness and use a donut cutter to shape your donuts.

Heat vegetable oil in a heavy pan to 350°F (175°C). Carefully place the donuts in the hot oil, frying them for 1 to 2 minutes per side until golden brown.

In a mixing bowl, whip the heavy cream, powdered sugar, and vanilla extract together until stiff peaks form.

Allow the fried donuts to cool completely before filling. Use a skewer to create a hole and fill with the prepared cream using a piping bag.