To a large pot or Dutch oven over medium heat, add the chopped bacon. Cook until crispy, about 8-10 minutes. Use a slotted spoon to remove the bacon from the pan and place it onto a plate. Reserve 2 tablespoons of bacon grease in the pot; discard the rest.
To the same pot with the bacon grease, add onion and jalapenos. Cook until softened, about 5–7 minutes.
Add garlic and cook for 1 minute.
Sprinkle flour over the top of the vegetables, stirring to combine, until no dry spots remain.
Slowly pour in the chicken broth and heavy cream, stirring constantly, and bring to a gentle simmer, about 5 minutes.
Reduce heat to low. In a heatproof bowl, whisk the cubed cream cheese with ½ cup of the hot broth mixture until completely smooth. Pour the cream cheese mixture back into the pot.
Add the shredded cheddar cheese, stirring until melted and the soup is smooth and creamy.
Season with kosher salt, black pepper, and red pepper flakes. Fold in half of the cooked bacon, reserving the rest for topping.
Keep the soup warm on low heat while you make the grilled cheese dippers.