In a large pot over medium heat, add the bacon and cook until the fat renders out and the bacon is very crispy, about 6-8 minutes, stirring occasionally. Transfer the bacon to a paper towel lined bowl or plate. Remove all but 1 tablespoon of the bacon grease (I just pour it into a can or ceramic bowl).
Add the onion, carrot, celery, and ½ teaspoon salt and stir to combine, scraping up any bacon bits stuck to the pot. Cook until the veggies have softened, about 3-5 minutes, stirring occasionally.
Stir in the smoked paprika, thyme, and red pepper flakes (if using) and cook for 30 seconds, stirring constantly. Add in the water, milk, potatoes, beans, soy sauce, and remaining 1 teaspoon salt. Stir to combine then bring to a boil over high heat. Once it’s boiling, reduce the heat to medium-low to maintain a rapid simmer for 15 minutes, stirring halfway, or until the potatoes are very soft.
Add 2-5 cups (depending on how creamy/thick you want it) of the potatoes/beans and broth to a high-speed blender (or use an immersion blender). Blend, then stir back into the pot along with the greens. The residual heat of the soup is usually enough to soften the greens, but you can simmer them if needed.
Serve topped with sour cream or yogurt, bacon bits, cheddar, green onions, and black pepper.