Choose your method: Stovetop for fast (30–40 minutes), or slow cooker for hands-off (4–6 hours on low).
Dump the base ingredients: Add chicken, corn, potatoes, onion, garlic, green chiles, broth, thyme, smoked paprika, salt, pepper, and bay leaf (if using) to your pot or slow cooker.
Stovetop cook: Bring to a boil, then reduce to a steady simmer.
Cover and cook 18–22 minutes, until the chicken is cooked through and potatoes are tender.
Slow cooker cook: Cover and cook on low for 4–6 hours or on high for 2–3 hours, until the chicken shreds easily and potatoes are soft.
Shred the chicken: Remove chicken to a plate and shred with two forks. Return it to the pot. If using pre-cooked or rotisserie chicken, add it now and heat through.
Make it creamy: Whisk cornstarch or flour into the cold half-and-half until smooth.
Stir this slurry into the chowder. Simmer 3–5 minutes (stovetop) or cook 20–30 minutes more (slow cooker) until slightly thickened.
Add richness: Stir in butter and a small splash of honey or sugar if you like a sweeter balance with the corn.
Taste and adjust: Add more salt, pepper, or smoked paprika to taste. For extra heat, a dash of hot sauce works well.
Serve: Ladle into bowls and top with scallions, bacon, cheddar, or a crack of black pepper.