Heat olive oil in a Dutch oven over medium heat. Stir in onion and celery; cook until translucent and soft, 5 to 7 minutes. Add potatoes, cover, and cook until beginning to soften, about 5 minutes. Stir in corn, bouillon, marjoram, parsley, a generous amount of salt, and pepper; cover and cook until corn is warmed through, about 2 minutes. Stir in flour; cover and cook 2 minutes more.
Stir almond milk and chicken stock into vegetable mixture; cover and bring to a boil. Lower heat and simmer until potatoes are tender and soup is thickened, 15 to 20 minutes. Remove from heat and cool slightly, about 5 minutes.