Warm the milk in a saucepan over medium heat until tiny bubbles form around the edges (do not boil).

Remove the pan from the heat and pour the warm milk into the bowl of an electric mixer.

Add the active dry yeast and about ¼ teaspoon of the cane sugar, stirring once or twice.

Let the yeast rest in the warm milk for 5 to 10 minutes until the mixture looks bubbly and highly active.

Stir in 2 cups of the all-purpose flour, cover the bowl with plastic wrap, and set in a warm place to rise for 30 minutes.

In a separate bowl, whisk together the 4 whole eggs and 1 egg yolk until pale and frothy.

Whisk the remaining cane sugar, vanilla extract, and kosher salt into the eggs.

Using a dough hook attachment on your electric mixer, blend the risen yeast mixture with the egg mixture.

Pour in the melted butter and mix until fully combined.

Gradually add 3 more cups of flour, one cup at a time, allowing the dough to come together around the hook. (You may add up to 1 more cup of flour if necessary, but the dough should remain sticky and loose).

Transfer the dough into a large bowl coated with vegetable oil spray.

Cover tightly with plastic wrap (sprayed with oil on the inside) and let the dough rise in a warm place until doubled in size, about 1 hour.

Sprinkle your work surface and rolling pin generously with flour.

Roll the proofed dough out to about ½-inch thickness.

Use a 3-inch round cookie cutter to punch out the donuts, placing them onto a parchment-lined baking sheet.

Gather any dough scraps, re-roll, and cut until all the dough is used.

Cover the cut donuts lightly with sprayed plastic wrap and let them rise in a warm spot until roughly doubled in size, about 30 minutes.

Heat the vegetable oil to 350°F in a deep fryer or heavy-bottomed pot (fill the pot only ⅓ full to allow for expansion).

Carefully lower 2 to 3 donuts into the hot oil so they swim freely without overcrowding.

Fry until the bottoms are deep golden brown, then use a slotted spoon to flip them and brown the other side (this only takes 1 to 2 minutes per side).

Transfer the fried donuts to a wire rack or a baking sheet lined with paper towels to drain excess oil.

Once the donuts are cool enough to handle, use a squeeze bottle or a piping bag fitted with a long tip to gently inject a burst of raspberry preserves into the center of each donut.

Dust heavily with confectioners' sugar before serving warm.