Heat 1 tablespoon butter and 1 tablespoon oil in a large, deep skillet or Dutch oven over medium high. Once the butter is melted, add the chicken and sprinkle with ¼ teaspoon salt and black pepper. Saute until the chicken is golden on the outside and completely cooked through, about 5 minutes. With a large spoon, remove the chicken to a plate and cover to keep warm. Set aside.
Reduce the heat to medium. Add the remaining 2 tablespoons butter and the onion. Cook until the onion begins to soften, about 3 minutes. Do not let the onion brown (adjust the heat as needed if it starts to brown). Add the garlic, Italian seasoning, red pepper flakes, and remaining ¼ teaspoon salt. Stir and cook just until fragrant, about 30 seconds.
Slowly stir in the broth and milk. Bring to a boil, then add the ziti. Let the ziti boil for 5 minutes, then stir in the broccoli florets. Continue boiling until the ziti is al dente, about 5 to 7 minutes more. Stir often to make sure the ziti cooks evenly. If at any point the pasta looks too dry, splash in additional milk as needed.
Stir in the artichoke hearts, lemon juice, Parmesan, parsley, and reserved chicken. Taste and adjust seasoning as you like. Enjoy hot, with a sprinkle of extra Parmesan and parsley as desired.
