Place the pepperoni in the food processor and pulse until very finely chopped. It should resemble bacon bits. Transfer to a bowl and set aside.
To make the doughnuts, place the warm milk in a large bowl or glass measuring cup. Add a pinch of the sugar and stir in the yeast. Set aside and allow to foam and froth up, about 10 minutes. If the yeast doesn't foam up, toss and start over.
In the bowl of a stand mixer, combine the flour, sugar, salt, butter, eggs, and yeast mixture. Mix on low until the dough starts to come together. Increase the speed and knead on high until the dough becomes smooth, soft and pulls away from the sides of the bowl, about 8 minutes. If it is too wet, you can add more flour, a tablespoon or two at a time until the desired consistency is reached. Sprinkle in the 1/3 cup of parmesan cheese and the chopped pepperoni from earlier. Knead the dough by hand in the bowl until the cheese and pepperoni are evenly distributed. Transfer the dough to a lightly greased bowl, cover loosely with plastic wrap and a damp kitchen towel. Place in a warm spot and allow to double in size, about 1 hour.
Line two baking sheets with parchment paper and dust each lightly with flour, set aside. Once risen, gently punch the dough down and then transfer to a well-floured work surface. Roll out to about 1/2 of an inch thick. Using a 3-inch doughnut cutter, cut out the dough into doughnuts and place onto the prepared baking sheets, spacing them out. Don't forget about the doughnut holes! Knead any scraps together, being careful not to overwork the dough, and let rest for a few minutes before repeating the cutting process. Cover the baking sheets loosely with plastic wrap or a damp kitchen towel. Allow to rest in a warm spot until slightly puffed up, about 45 minutes.
About 15 minutes before the doughnuts are done rising, put the oil in a heavy-bottomed pot or Dutch oven over medium heat, and heat it to 375°F. Meanwhile, line cooling racks, baking sheets or plates with paper towels.
Once the oil has reached the correct temperature, carefully add the doughnuts, a few at a time. Do not over-crowd the pot. When the bottoms are golden, after 45 seconds to a minute, use a slotted spoon to flip over; cook until they’re deep golden all over. Transfer to the prepared plates or racks, and repeat with the rest of the doughnuts, adjusting the heat as needed to keep the oil at 375°F. Lastly, fry the doughnut holes all at once, turning them often to get them evenly browned. Just note that the holes will fry much faster.
In a shallow dish, toss together the parmesan, Italian seasoning, basil, parsley, oregano, red pepper, garlic, salt and pepper until evenly combined. While the doughnuts are still warm, toss in the cheese mixture to evenly coat both sides. Transfer to a platter. Top with fresh basil and serve with warm pizza sauce for dipping. Doughnuts are best eaten the day they're made. Enjoy!