In a large pot, over medium heat, add a splash of oil and sauté the diced jalapeños, onion, and garlic until soft and fragrant, about 5 minutes.

Pour in the chicken or vegetable broth and raise the heat until it begins to simmer.

Stir in the cream cheese and milk until they blend together smoothly.

Add the shredded sharp cheddar cheese and stir until it melts into the soup. Season with salt and pepper to taste.

Butter two slices of bread and place a slice of cheddar cheese between them.

In a skillet, grill the sandwich until golden brown and the cheese is melted.

Ladle the soup into bowls and cut the grilled cheese into strips for dunking. Serve warm.