Step 1: Arrange a rack in center of oven; preheat to 375°. In a large pot of boiling salted water, cook pasta, stirring occasionally, until al dente according to package directions, 8 to 10 minutes. Drain.

Step 2: In a large, high-sided, cast-iron or other ovenproof skillet over medium heat, heat oil. Cook onion and jalapeño, stirring occasionally, until onions are softened, about 7 minutes; season with 1/2 tsp. salt. Add garlic, paprika, and cumin and cook, stirring, until fragrant, about 1 minute more.

Step 3: Add butter and cook, stirring, until melted and foamy. Add flour and cook, whisking frequently, until dissolved and toasty smelling, 1 to 2 minutes.

Step 4: Add broth and cream, whisking until no lumps remain. Bring to a low simmer and cook, whisking occasionally, until slightly thickened, 1 to 2 minutes. Reduce heat to medium-low and add 1 1/2 cups Gouda and 1 1/2 cups cheddar, stirring until melted. Fold in chicken, beans, corn, and pasta; season with salt and pepper. If skillet seems dry, add more broth, if needed. Sprinkle remaining 1/2 cup gouda and 1/2 cup cheddar over.

Step 5: Transfer skillet to oven and bake chili until golden brown on top and bubbly around the edges, 25 to 30 minutes. Top with cilantro.