Season chicken with Cajun seasoning, using about 1/2 tsp per side, then let it rest at room temperature for 10 to 15 minutes.
Heat avocado oil in a large nonstick pan over medium heat and cook the chicken for 4 to 5 minutes per side until browned and cooked through; remove and keep warm tented with foil.
In the same pan, sauté zucchini, bell pepper, and jalapeno for 6 to 7 minutes until softened, scraping up any browned bits.
Add tomatoes, half the green onions, tomato paste, and a pinch of salt; cook for about 5 minutes, stirring occasionally.
Start boiling the farfalle pasta in salted water and cook until al dente, about one minute less than package instructions.
Stir in garlic and crushed red pepper, cook for 1 minute, then reduce heat to medium-low and add half and half; simmer gently for 6 to 7 minutes until thickened, seasoning with salt and pepper.
Add the cooked pasta to the sauce and toss well to coat; grate in Parmesan cheese and stir to combine.
If needed, add reserved pasta water tablespoon by tablespoon to achieve desired creaminess.
Serve the pasta in warm bowls topped with remaining green onions, extra Parmesan, and crushed red pepper to taste.