Melt butter in a large pot over medium heat.
Add chopped onion and sauté until softened.
Stir in diced jalapeños and minced garlic; cook for 1 minute.
Sprinkle flour over vegetables and stir to coat evenly.
Slowly pour in chicken broth while stirring constantly.
Add milk and heavy cream, then bring to a gentle simmer.
Stir in cream cheese until fully melted and smooth.
Season with smoked paprika, salt, and black pepper.
Simmer the soup for 20 minutes, stirring occasionally.
Blend partially for a creamy but slightly chunky texture.
Stir in shredded cheddar cheese until melted.
Heat a skillet over medium heat for grilled cheese dippers.
Butter bread slices, add cheese, and grill until golden.
Cut grilled cheese into strips and serve with soup.