Bring a large pot of salted water to a rolling boil. Add the pasta and cook according to package directions until al dente. Reserve 1/2 cup of pasta cooking water before draining. Drain the pasta and set aside.

While the pasta cooks, pat the chicken cubes dry with paper towels. Season with 1/2 tsp salt and 1/4 tsp black pepper. Heat 1 tbsp olive oil in a large skillet over medium-high heat. Add the chicken and cook for 5-7 minutes, stirring occasionally, until golden brown and cooked through. Remove chicken from the skillet and set aside.

In the same skillet, add the remaining 2 tbsp olive oil. Reduce heat to medium. Add the diced yellow onion and cook for 3-4 minutes until softened. Add the minced garlic, red bell pepper, and broccoli florets. Sauté for 5-7 minutes, stirring frequently, until the vegetables are tender-crisp. Add the sliced zucchini and cook for another 2-3 minutes.

Pour in the chicken broth and lemon juice. Bring to a simmer, scraping up any browned bits from the bottom of the pan. Stir in the grated Parmesan cheese and red pepper flakes (if using). Add the cooked chicken, drained pasta, thawed peas, halved cherry tomatoes, and fresh spinach to the skillet. Toss gently until the spinach wilts and all ingredients are well combined and heated through. If the sauce seems too thick, add a splash of the reserved pasta water until it reaches your desired consistency.

Season with additional salt and black pepper to taste. Garnish with fresh chopped parsley and extra grated Parmesan cheese before serving warm.