Put a large pot of salted water on high heat and bring it to a boil. Cook the pasta until it’s tender but still firm, then save 1/3 cup of the pasta water before draining.
While the pasta cooks, heat a tablespoon of olive oil in a big skillet over medium-high heat. Season the chicken pieces with salt and pepper, then cook until they turn golden and are fully cooked, about 6 to 8 minutes. Remove the chicken and set aside.
In the same skillet, add a bit more olive oil if needed. Toss in the bell pepper, zucchini, broccoli, and snap peas. Cook these veggies for 5 to 6 minutes until they soften but still have a bit of crunch.
Add the minced garlic, oregano, red pepper flakes if using, and cherry tomatoes to the pan. Stir and cook for 2 minutes more to blend the flavors.
Turn the heat down to medium-low, push the vegetables to one side of the skillet, and melt the butter with the olive oil on the empty side.
Combine the cooked pasta, chicken, parmesan cheese, lemon juice, and a splash of the reserved pasta water with the veggies and melted butter. Toss well to coat everything in a creamy sauce, adding more pasta water if it seems dry.
Serve the pasta warm with extra parmesan and a sprinkle of fresh parsley or basil. Finish with a fresh squeeze of lemon juice for bright flavor.
