Heat a large Dutch oven or pot over medium heat. Add the bacon and cook, stirring occasionally, until crisp, 12 to 14 minutes. Transfer the bacon to a plate with a slotted spoon; set aside to uselater as a topping.
Leave 1 tablespoon of the bacon fat in the pot. Over medium heat, add the butter. Once melted, stir in the celery, onion, and carrot cook, stirring occasionally, until the vegetables have softened, about 10 minutes.
Stir in the potatoes and season well with salt and pepper. Add smoked paprika and chile powder (or hot smoked paprika). Cook, stirring, for 2 minutes. Add the broth, increase the heat to high and bring to a boil. Cover, reduce heat to medium-low and simmer, stirring occasionally, until the potatoes are fork tender, 15 to 20minutes. As the soup simmers, taste the broth and add salt If needed. Stir in as much heavy cream as you like and remove from the heat.
Use an immersion blender and blend about half the soup in the pot. Add more heavy cream, salt and pepper, if desired, and serve in bowls topped with bacon, and cheese.