Heat olive oil in a large pot over medium-high heat. Saute leeks until translucent, 3 to 5 minutes. Add potatoes, parsnips, turnip, celery, and carrots. Cook and stir until slightly tender and coated in oil, about 4 minutes. Add garbanzo beans, vegetable broth, beer, and parsley. Bring stew to a boil.
Reduce heat to low; cook until vegetables are tender and stew thickens slightly, about 1 hour more. Add a little water if necessary. Season with salt and pepper.
