In a saucepan, melt butter and add onion and celery. Cover and cook on medium heat, stirring occasionally, so it does not burn,
While that is cooking, dice the potatoes and begin boiling those in some water, about 2 cups, but no need to measure. When the potatoes begin boiling, turn the heat down and check occasionally to see if they are tender. When they are tender, drain and set aside.
When onions and celery are tender, combine cornstarch with 1 cup water. Add to pan with chicken base and milk. Stir so there are no lumps. Add salt, pepper and parsley as it cooks. Cook over medium heat, stirring often, until it is thickened as desired. Add potatoes and stir in. Rewarm for a few minutes, if necessary, and serve.
Suggested garnishes are fresh parsley or cilantro, shredded cheese of your choice, bacon (cooked and crumbled) or croutons (be careful of the croutons if gluten free or wheat free).