First we will begin making the dough. Heat up milk in a small sauce pan until it begins to simmer. Remove from heat and add sugar and salt and stir. Let it cool down to lukewarm to the touch. While milk is cooling, proof the yeast by adding the warm water and yeast in a small bowl and stirring together. Let it activate by setting it aside for 10 minutes.
Once milk is cool, add to a large bowl, along with 2 1/2 cups of the flour, 2 tablespoons of oil, eggs, and yeast mixture. Stir together with a wooden spoon until combined. The dough will be very thick but still wet and sticky.
Place remaining 1 cup of flour on the surface of your counter. Place dough on top of it and begin kneading the dough with the flour until all the flour is mixed into the dough. Keep kneading for about 4-5 minutes until the dough is smooth and elastic. If it starts to stick to the counter, add a little more flour. Once you finish kneading, shape into a ball. Lightly grease another large bowl and place the ball of dough into bowl. Cover with a kitchen towel and let it rise for 1 1/2 hours, where it will be double the size. I like to place mine in the microwave to keep it away from any cool draft from the A/C.
When the doughnuts are rising, prepare the filling. First, place the softened cream cheese, milk, sugar, and vanilla in the bowl of a stand mixer with a paddle attachment. Mix on low to combine. Use a spatula to scrape down the sides to ensure it's all mixed together. Set aside until assembly.
Grab blackberries and place in a medium bowl. If they are super large like mine were, cut them in half. If not, leave them whole. Add 2 tablespoons of sugar and stir to combine. Place in fridge until assembly.
Once dough has risen, punch it down with your fist and remove from the bowl. Lightly dust your counter with flour and place the dough on top. Begin rolling out the dough into a large oval or rectangle that is 1/2-inch thick. Make sure to release it from the counter so that it's not sticking or stretching.
Using a 2 to 3 inch round cutter, cut out perfect rounds and place them on a lightly floured baking sheet(s). Make sure to leave about 1/2 inch between them so they don't stick together after rising. You will get about 15 rounds with the first pass at the dough. Gather the scraps in a ball and roll them out to get about 5-6 more rounds. Cover doughnuts with a kitchen towel and let them rise again for about 30 minutes.
While the doughnuts rise again, begin heating the frying oil. Place oil in a large pot or dutch oven and heat on medium-high until a candy/frying thermometer reaches 375 degrees. Then reduce heat to about medium. Fry doughnuts 4 at a time, 1 minute on each side. Continue to monitor temperature. Do not let it get below 350 degrees or above 380 degrees. Let doughnuts cool on paper towels to drain excess oil. Repeat until all doughnuts are fried.
Place 1/2 cup of superfine sugar in a paper bag. Place a doughnut in the bag 1 at a time and shake to cover the doughnut in sugar. Repeat with the rest of the doughnuts. Let them cool for 5 minutes