In the bowl of your stand mixer, mix together all the ingredients.
Mix on low speed using the dough hook. After about a minute, increase the speed to medium and knead for 10-15 minutes, or until the dough completely clears the sides of the bowl. It will still be gooey in the bottom, and you think it will never happen, but it will. Give it time.
Oil your hands well and gather the soft dough into a ball as best you can.
Oil a bowl and place the dough ball in it. Spray or brush the dough with some oil. Cover and let rise in a warm place (I boil water in the microwave and then move the mug to the back, making room for the covered bowl) until doubled, about 1 hour to 1 hour and 15 minutes.
Once the dough has risen, gently press out the gases and then roll it to a 1/2" thickness on a heavily floured surface.
Using a 3" cutter, cut circles out of the dough and place them on parchment-lined pans. From the first roll, you will get maybe 11-12 doughnuts. Gathered the scraps together, let them rest covered so the gluten can relax and then reroll to get 4 more rounds for a total of 15-16. You may get one or two more or less depending on how thick/thin you rolled.
Spray the doughnuts with some oil or pan spray and cover with plastic wrap. Let rise for about 30 minutes or until noticeably puffy.
In your heavy Dutch oven, bring the oil up to 360F.
Fry 2-3 doughnuts at a time. Fry on one side for about a minute, until the side that is down is doughnut colored. Flip with chopsticks or whatever is handy and fry another minute until the second side matches the first.
Remove to a rack with paper towels under it to drain and cool. Let them cool completely before filling and topping. This will take about 20-30 minutes.
Once cool, fill a pastry bag fitted with a Bismarck tip with the raspberry jam. Insert the tip all the way into one side of the doughnut. Slowly squeeze the bag and fill the doughnut while slowly pulling the tip out of the doughnut. Don't overfill. You want about 2 Tablespoons of filling per doughnut.