Remove the tenderloins (small muscle on the underside) from the chicken breasts. Cut the chicken breasts in half lengthwise. Cut all the chicken into 1 1/2-inch pieces. Season with 1 1/2 teaspoons salt and 1/2 teaspoon pepper.
Heat the oil in a large ovenproof pot over high heat. When the oil is almost smoking, add the chicken. Cook until well browned on 2 sides, turning once, 6 to 7 minutes total. Add the sausage to the pan. Cook for 10 seconds.
Season the shrimp with 1/2 teaspoon salt and 1/4 teaspoon pepper. Add the shrimp to the pan, stir once then cook for 2 to 3 minutes. Stir in 1 1/2 teaspoons paprika and the oregano. Pour the mixture onto a baking sheet to cool.
Return the pan to high heat. Add onions, carrots, and celery. Pour the juices from the baking sheet into the pan. Reduce the heat to medium-low. Cook until the vegetables are soft, but not brown, about 10 minutes, stirring occasionally.
Preheat the oven to 350 degrees F.
Raise the heat to high. Add 1 teaspoon salt, 1/2 teaspoon pepper, and remaining 2 teaspoons paprika. Cook for 2 minutes, stirring occasionally. Add the rice. Stir to evenly coat the grains with oil. Cook for 1 minute. Add the stock and bring it up to a simmer. Add the tomatoes and stir to incorporate. Sprinkle in the saffron. Taste and adjust the seasonings, if needed. Cook until the liquid comes back to a simmer. Cover and put the pan in the oven. Cook for 15 minutes. Remove the pan from the oven. Return the chicken, sausage, and shrimp to the pan. Cover the pan again and put it back in the oven to cook for an additional 10 to 15 minutes until everything is warm.
Serve the paella warm with a bowl of pepperoncini on the side. Invite guest to add a couple pepperoncini to the servings and drizzle some of their vinegar on the paella.