In a large pot, heat oil over medium-high heat. Add onion, carrots, and celery. Add salt and pepper as needed. Cook until onions are translucent and vegetables begin to soften, about 10 minutes.
Add rinsed peas, water, and thyme to the pot. Stir to combine and bring to a boil. Reduce heat to medium-low, and simmer, partially covered for 50-60 minutes, stirring occasionally, until peas and vegetables are soft.
Add ham and parsley, if using. Stir to combine and heat until warmed through. Season with salt and pepper as needed.