Green Beans with Potatoes and Ham

meaty ham hocks

onion, peeled and quartered through root

garlic cloves, smashed

celery stalk, cut into 2-inch pieces

sprigs fresh thyme

bay leaf

jalapeno or serrano chile, intact with a split down 1 side

Coarse salt and freshly ground pepper

water

small red potatoes, halved

green beans, stem ends trimmed, halved crosswise