In a large bowl or glass measuring cup, combine the milk and butter and microwave until warmed through. Do it in short 15 second bursts so as to not get it too hot. Set aside to cool slightly.

In the bowl of your stand mixer, fitted with the dough hook, combine the flour, sugar, salt, yeast, egg, and the warmed milk and butter mixture. Mix on low until the dough starts to come together. Increase the speed to high and knead until the dough pulls away from the sides of the bowl and is smooth, yet slightly sticky, about 5 minutes. If your dough is too sticky, you can add a bit more flour, a tablespoon at a time, until you reach the right consistency. Transfer the dough to a greased bowl and cover with plastic wrap and a damp kitchen towel. Allow to rest in a warm spot until doubled in size, about 2 hours.

In the meantime, to make the sauce, combine the raspberries, sugar, lemon juice and water in a medium saucepan. Set over moderate heat and cook, stirring often, until the berries have softened and the sauce has thickened, about 8 to 10 minutes. Remove from the heat and pour into a bowl through a fine mesh strainer. Use the back of a spoon to press the pulp and seeds down to get all of the sauce out. Discard the seeds and cover the sauce with plastic wrap; set aside.

Transfer the dough to a floured work surface and roll out to about 1/2-inch thick. Use a 4-inch round cutter to punch out the doughnuts. Then use a small round cutter (the backside of a small cake decorating tip works great) punch out a mouth and two eyes for every doughnut. Use your hands to slightly stretch the doughnut to create ghost shape. Place on a baking sheet lined with parchment paper. Cover loosely and let rest for about 30 minutes.

Fill a large cast iron skillet or heavy bottom pot with about 2 inches of oil and bring up to 350°F. Once hot, carefully lay in about 3 doughnuts at a time. Cook until golden brown, about 3 to 4 minutes per side. Use a slotted spoon to transfer the doughnuts onto a plate lined with paper towels. Continue to fry the remaining doughnuts, making sure the temperature is at 350°F before each batch fries.

Once all the doughnuts are done, dust them liberally with powdered sugar and serve with the raspberry sauce on the side for dipping.