Cut 1/2-inch incisions into the meaty parts of the roast; stuff with shallots and garlic. Season roast with salt and pepper; top with thyme sprigs.
Center roast in a large roasting pan. Pour in water and beef broth. Spread carrots and celery around the roast. Cover and marinate in the refrigerator, 8 hours to overnight.
Preheat oven to 300 degrees F (150 degrees C).
Place potatoes in a large bowl; cover with water. Let soak, 10 to 15 minutes. Drain and pat dry. Add rosemary and olive oil; toss to coat. Spread potatoes around the roast.
Bake in the preheated oven until potatoes are very tender, about 3 hours.
Reduce oven temperature to 250 degrees F (120 degrees C). Continue baking until an instant-read thermometer inserted into the center of the roast reaches 145 degrees F (65 degrees C), about 1 hour more.
