Pour in the broth and bring to a simmer. Break up the cream cheese into chunks and whisk into the simmering broth until fully melted and smooth, about 3–4 minutes. If using sour cream, whisk it in now for extra tang.
Stir in milk (or half-and-half) and corn. Simmer gently for 5–7 minutes, until the soup is creamy and just coats the back of a spoon. If it thickens too much, add a splash more broth or milk.
Fold in shredded cheddar and let it melt, stirring until the soup is glossy and velvety. Season with salt, pepper, and a pinch of smoked paprika or cumin if using. Taste and adjust heat with extra jalapeño or a dash of hot sauce if you like.
For a creamy texture with a bit of body, use an immersion blender to partially puree the soup right in the pot (about half the soup). Leave some chunks for texture, or blend until smooth if you prefer a silkier finish.
Meanwhile, make the grilled cheese dipper: Butter the bread slices on one side and layer with a little extra cheddar. Grill in a skillet over medium heat until the bread is deeply golden and the cheese inside has melted. Let cool briefly, then cut into thick strips.
Ladle the soup into bowls and top with a swirl of extra sour cream if desired, a sprinkle of cilantro or green onions, and a dusting of paprika. Serve hot with the grilled cheese dippers on the side for dipping.
Notes
A cozy, creamy soup that blends jalapeño heat with creamy cheese and cheddar, served with crispy grilled cheese dippers for dipping.
