In a small bowl, combine warm water and yeast. Let it sit for about 5 to 10 minutes until it's frothy.

In a large mixing bowl, combine the warmed milk, melted butter, sugar, and the activated yeast mixture. Whisk in the egg until well blended.

In another bowl, whisk together the flour and salt. Gradually add this to the wet ingredients, stirring until a dough forms.

Lightly flour a clean surface, turn out the dough, and knead it for about 5 minutes until smooth and elastic. If the dough is sticky, add a little extra flour as needed.

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

Once risen, punch the dough down and roll it out to about 1/2 inch thickness. Use a donut cutter (or two round cutters) to cut the donuts and holes out.

Place the shaped donuts on parchment paper and cover them again. Let them rise for another 30 minutes.

In a deep pot or fryer, heat vegetable oil to 350°F (175°C).

Carefully add the donuts to the hot oil, frying them for about 1-2 minutes on each side until golden brown. Make sure not to overcrowd the pot.

Once donuts are cool enough to handle, use a piping bag or a small injector to fill them with raspberry jelly. Dust with powdered sugar before serving.