Add 1 can (15 ounces / 425 grams) of white beans and 1 cup (240 milliliters) of water to a blender. Blend on high until completely smooth.
Turn on the saute function of your electric pressure cooker. Add the chopped bacon and cook until crisp. For food safety, ensure pork products reach an internal temperature of 145°F (63°C) with a 3-minute rest, though bacon is visually cooked until crisp. Remove the bacon to a paper towel-lined plate and leave the bacon fat in the pot.
Add the chopped onions, carrots, and celery to the pot. Saute for about 5 minutes until the vegetables soften.
Stir in the tomato paste and cook for 1 minute to coat the vegetables.
Pour in the pureed bean mixture, the remaining 2 cans of drained whole beans, chicken broth, Italian seasoning, red pepper flakes, and black pepper. Stir well to combine.
Secure the lid and set the valve to sealing. Cook on high pressure for 20 minutes.
When the timer finishes, turn the cooker off and let the pressure release naturally for 10 minutes, then carefully vent any remaining pressure.
Transfer 2.5 cups (600 milliliters) of the hot soup to a blender. Puree until smooth, then stir it back into the pot to thicken the soup.
Ladle the soup into bowls. Top each serving with the reserved crisp bacon and chopped chives.