Combine the buttermilk, sugar, and yeast in a large bowl. Whisk to dissolve the yeast. Leave for 5-10 minutes until foamy.
¾ cup buttermilk, 2¼ teaspoons active dry yeast, 3 tablespoons granulated sugar
Add in the eggs, vanilla, and salt, and stir until combined.
3 large eggs, 1 teaspoon pure vanilla extract, ½ teaspoon kosher salt
Add the flour. Mix using the dough hook attachment on a stand mixer (or by hand). Knead on low-medium speed for about 3 minutes, or until it forms a ball around the hook.
4 cups all-purpose flour
Slowly incorporate the butter cubes, one piece at a time, and knead well. The dough should to be glossy and smooth.
9 tablespoons unsalted butter
Once all of the butter is incorporated, turn the mixer up to medium speed and knead for 10-12 minutes, until smooth and elastic.
Transfer the dough to a lightly greased bowl, cover with plastic wrap, and allow to proof in a warm, draft-free place for about 1 hour, or until doubled in size.
Punch the dough down and turn it out onto a lightly floured surface. Use a rolling pin to roll to about ½-inch thickness, and use a donut cutter to cut out donuts (save the donut holes).
Cover them with plastic wrap as you re-roll and cut out the remaining dough. Allow the donuts to proof at room temperature for 30-45 minutes, or until puffy.
Fill a Dutch oven at least 2-3 inches deep with oil and heat to 350-360°F. Fry the donuts, three at a time, for 30 seconds on each side for a total of about 2-3 minutes (about 1 minute for the donut holes).
Vegetable oil
Remove donuts from the oil with the spider tool and place on a tray lined with paper towels.
Once slightly cooled, toss each donut in the bowl of cinnamon sugar, and set aside to cool.
⅔ cup granulated sugar, 2 tablespoons ground cinnamon