Heat the milk in the microwave for 15-20 seconds. Add the yeast and 1 tsp of sugar. Stir gently to combine and let it rise for 5 minutes.
To a large stand mixer bowl, (or a large bowl, if using a hand mixer with a dough hook), add 2 cups of flour, 4 tablespoons + 2 tsp sugar and salt. Stir to combine. Add eggs, yeast, milk, and vanilla. Knead over low speed for 2 minutes to combine.
While mixing, add the butter slowly, 1 tablespoon at a time.
Gradually add the remaining 1 cup of flour and more if needed. Knead until soft and smooth. Transfer to a floured surface and knead for 5 more minutes.
Add the dough to a greased bowl covered with a clean cloth and let it rise in a warm place for 1 hour, or until doubled in size.
With floured hands, remove the dough from the bowl gently and roll to ½ or ¾ inch thickness. Cut into rounds using a 3 ½ inch floured dough cutter.
Reroll scraps as needed. Add rounds to a parchment paper tray and cover with a cloth. Let it rise in a warm area for 40 to 50 minutes more until doubled in size.
When ready to fry, add 2-3 inches of oil to a heavy bottomed pan at medium heat. Fry donuts for 1-2 minutes each side until golden brown, turn and repeat.
Transfer to a paper towel lined plate.
Add 1/2 cup sugar and 2 tablespoons pumpkin spice, or more to taste, to a large bowl and mix. Add donuts and toss to coat. The sugar mix will stick better to the donuts when hot and some oil is still on it.
Add the refrigerated pumpkin filling to a piping bag fitted with a ¼ inch round tip. Pierce each donut horizontally through the center and gently swirl to widen the hole. Squeeze piping bag to fill donut with pumpkin filling.
Heat dark chocolate chips in microwave for 10 seconds at a time until it melts. Make sure to mix each time. Drizzle tops of donuts with dark chocolate. Enjoy!