In a bowl, mix together warm milk and yeast, and then let it sit for several minutes to activate the yeast.

Add the sugar, melted butter, eggs, salt, and vanilla, and mix well.

Add the flour and mix with a dough hook until it forms a ball and pulls away from the sides.

Remove the dough from the bowl and knead by hand for an additional 5 minutes.

Lightly coat a large bowl with oil or cooking spray. Place the dough in the bowl and cover with a clean kitchen towel. Leave in a warm spot for about 1-½ hours or until the dough has doubled in size.

While the dough is proofing, make the filling by mixing together brown sugar, cinnamon, and softened butter until it forms a paste.

Once the dough has doubled in size, roll it out on a lightly floured surface until it measures approximately 14" x 20".

Spread the filling across the entire surface of the dough.

Fold the dough in half and slice it into 12 equal strips.

Twist each of those dough strips several times and pinch the ends tightly together.

Place formed doughnuts on a lined tray and cover lightly with a towel. Let them rest for about 30 minutes.

Heat the canola oil in a pot to reach between 350℉ and 375℉.

Fry the donuts one at a time for 40 seconds on one side, then turn and cook for 20 seconds on the other side.

Remove from the pot and place on a wire cooling rack.

For the cream cheese frosting, mix softened cream cheese, powdered sugar, melted butter, and vanilla extract until smooth.

Once the donuts have cooled, drizzle or spread the frosting over them.