Heat the oil and saute the onion a few minutes, until softened. (I do this while I'm prepping the garlic, carrots, and celery.) Add the garlic and stir, cooking a minute or so.
Add the celery and carrots and stir. (At this point I peel and dice the potato, letting the other vegetables cook.)
Add the both, potato, green beans, thyme, salt and pepper.
Bring to a simmer and cook until the potatoes and carrots are cooked through.