In stockpot over medium-high heat, add oil. Add onion, celery, and green and red pepper. Sauté until onion is translucent, 3 to 5 minutes.
Reduce heat to medium. Add flour. Whisk until well blended. Cook, whisking often, 4 minutes. Do not brown. Stir in base.
Add water. Whisk until well blended. Cook, whisking constantly, until mixture thickens and boils.
Add remaining ingredients. Return to a boil. Reduce heat. Simmer until potato is tender, 20 to 25 minutes.
Heat milk and stir into soup. Return to a simmer. Do not boil.
Remove from heat and cover. Serve hot.