In a small mixing bowl, combine the warm water and instant yeast. Let it set for about 5-10 minutes to allow the yeast to become foamy.
In a stand mixer bowl, add the flour, powdered sugar, salt, nutmeg, and cardamon. Give the dry ingredients a stir using a spatula.
Next, add egg yolks, 2 tablespoons of vegetable oil, and vanilla extract to the yeast mixture. Stir to combine.
Place a dough hook on your stand mixer, then add the wet ingredients to the dry ingredients. Turn the mixer to low and gently combine the dough until it comes together.
Spray a large mixing bowl with non-stick spray and place the dough into the bowl. Cover with plastic wrap until it has doubled in size, about 1-2 hours. Next, line a baking sheet with parchment paper or a silicone baking mat, and dust with all-purpose flour.
Clear a work surface and dust with flour before placing the dough on top. Using a rolling pin, roll out the dough into a large rectangle about ¼-inch thick.
Take a 3-inch cookie cutter and cut out circles. Place the circles on the floured baking sheet. Cover the baking sheet with plastic wrap and let the circles rise again for at least 15-20 minutes.
Meanwhile, add vegetable oil to a large Dutch oven. You'll want about 2 inches of oil in the pot. Place a candy thermometer in the pot and heat the oil to between 325 and 375˚ Fahrenheit. While waiting for the oil to reach temperature, prepare a plate lined with paper towels.
Using a spatula, carefully place the dough into the oil. Fry on one side for about a minute and then flip and continue to fry on the other side for about a minute.
Remove the doughnut and place on the prepped plate. Repeat the process until all the circles have been fried.
Once the doughnuts have cooled, use a paring knife to make a small slit in the side of the doughnut. Next, use a piping bag to squeeze some of the apple butter into the doughnut. You'll know it's full when the apple butter starts coming out of the hole. Once all the doughnuts have been filled, dust each one with granulated sugar and powdered sugar. Serve and enjoy.
