Heat 1 tablespoon butter and 1 tablespoon olive oil in a large deep skillet or Dutch oven over medium-high heat until the butter melts.
Add the chicken strips, sprinkle with 1/4 teaspoon kosher salt and 1/4 teaspoon black pepper, and sauté until golden and cooked through, about 5 minutes.
Transfer the cooked chicken to a plate and cover to keep warm.
Reduce heat to medium and add the remaining 2 tablespoons butter and the chopped onion; cook until the onion softens, about 3 minutes, without browning.
Add the minced garlic, Italian seasoning, red pepper flakes, and the remaining 1/4 teaspoon salt; stir and cook until fragrant, about 30 seconds.
Slowly pour in the chicken broth and milk, then bring the mixture to a boil.
Add the dry ziti to the boiling liquid and boil for 5 minutes, stirring occasionally to prevent sticking.
Stir in the broccoli florets, then continue boiling until the pasta is al dente and the broccoli is tender, about 5 to 7 minutes more; add extra milk by the splashful if the pan looks too dry.
Stir in the drained artichoke hearts, lemon juice, grated Parmesan, chopped parsley, and the reserved chicken; heat through and taste, adjusting seasoning as needed.
Serve hot with extra Parmesan and parsley sprinkled on top if desired.
