Create a roux by melting butter in a large pot over medium heat, then whisking in the flour. Stir constantly for 1-2 minutes to cook out the raw flour taste.
Gradually whisk in the chicken broth to ensure a lump-free base. Once smooth, slowly stream in the room temperature half-and-half until fully incorporated.
Incorporate the shredded chicken, sausage rounds, drained red beans, corn, and diced green chilies.
Season the chili by adding the onion flakes, garlic powder, cumin, chili powder, cajun seasoning, and smoked paprika, stirring well.
Bring the mixture to a gentle simmer before reducing the heat to low. Let it cook for 20-30 minutes, stirring occasionally, to let the flavors meld.
Remove the pot from the heat and mix in the shredded pepper jack cheese until it's melted and the chili is creamy. Serve hot and enjoy.