Toss the cauliflower florets, carrots, onion, garlic cloves, black pepper, dried rosemary, and olive oil together until everything is evenly coated.
Add to an air fryer basket or sheet pan. Air fry at 400ºF for 35-40 minutes, shaking every 10-15 minutes, until the carrots and onion are tender and the cauliflower is slightly brown around the edges. Or bake on a sheet pan at 400ºF for 50-60 minutes.
Transfer the carrots to a bowl, placing the remaining cauliflower, onion, and garlic in the Instant Pot set to sauté or in a soup pot over medium-high heat. It's okay if a few carrots go in.
Add the broth, water, and milk. Use an immersion blender to blend until smooth. (You can also use a blender or food processor.)
Once smooth, bring the pot to a boil before reducing to a simmer.
Add the chicken, peas, and carrots. Stir everything together and once the peas have come up to temperature after 5-10 minutes, salt and pepper to taste.