Inspect peas, discarding any stones, foreign matter, or unattractive peas. Place peas in a fine mesh strainer and rinse under cold running water to remove pea dust.
Transfer drained peas into a pot with a lid and a heavy, heat-diffusing bottom. Add water, onion, celery, ketchup, olive oil, salt, garlic, and bay leaves. Cover and bring to a boil over medium-high heat. Reduce heat to a very slow simmer. Cook, stirring and scraping the bottom every 7 to 12 minutes, until peas have largely fallen apart, about 1 1/2 hours.
Stir carrots into the soup. Cook, covered, stirring often, until peas are completely dissolved and soup is thick, about 1 1/2 hours more. Remove and discard bay leaves. Season with pepper.
If the soup reduces too quickly before the peas are falling apart, add a 1/2 cup more water in Step 2. (And lower the heat under the pot.)
As the soup thickens again in Step 3, the risk of scorching can increase. Set the lid of the pot very slightly ajar to allow heat and steam to escape. Or reduce the flame to a poach (slower than a simmer: no bubbles, but active steam). Or place a heat diffuser under the pot. In any case, stir a little more often.