Heat 1 ½ tablespoons of olive oil in a large cast iron or other skillet over medium high heat. Add the onion and salt to the skillet and stir to coat the onion in the olive oil and saute until the onion is soft and just starting to brown a little. Add the garlic and stir for 20 seconds. Remove to a plate.
Add ½ tablespoon of olive oil and brown the mushrooms quickly. Remove to a plate.
Sprinkle the chicken with salt and pepper. Add 1 tablespoon of olive oil to the skillet and brown the chicken thigh pieces in two batches, turning over when the chicken is browned on the first side. Turn over and cook until browned on the bottom and chicken pieces are almost cooked all the way through. Remove to a bowl and cover with a plate to keep warm.
With the burner on medium high temperature, add the wine and stir and scrap the bottom of the pan to get the bits off the bottom. Stir in the chicken broth and the limoncello. Add the tomatoes and low the heat to a simmer, stirring often. Stir in the onion and garlic, tomato paste, fresh herbs, and dried basil. Cover and simmer over very low heat for 20 minutes. Add the chicken pieces back into the skillet along with the artichoke pieces, mushrooms, and dairy free butter and continue cooking for 5-8 minutes more.
Boil water in a stockpot. Add 1 teaspoon of oil. Stir in the Veneziane capellini nests and cook al dente. Drain, rinse gently and drizzle with olive oil. Pour into a large flat bowl and top with sauce. Serve with freshly grated Pecorino cheese for those who can have dairy.