Heat oven to 400°F. Butter an 8-inch skillet or square pan for cornbread.
Whisk flour, cornmeal, sugar, baking powder, and salt in a bowl. Stir in milk, beaten egg, and melted butter. Fold in honey if using.
Pour batter into the prepared pan and bake 18–22 minutes, until golden and a tester comes out clean. Cool slightly.
Warm olive oil in a large pot over medium heat. Add onion and jalapeño; cook until softened, 5–6 minutes.
Stir in garlic, cumin, chili powder, oregano, coriander, salt, and pepper. Toast the spices for 30 seconds.
Pour in chicken broth and green chiles. Bring to a simmer.
Add shredded chicken, beans, and corn. Simmer gently 12–15 minutes to meld flavors.
Lower heat. Stir in cream cheese until smooth, then add half-and-half. Warm without boiling, 2–3 minutes.
Finish with lime juice and cilantro. Taste and adjust salt and pepper.
Ladle chili into bowls and serve with warm cornbread on the side.