Heat the oil in a large stockpot over medium-high heat. When the oil is hot, brown the rabbit on both sides, seasoning each side with salt and pepper. This should take about 8 minutes total.

Tie the bay leaf and the thyme together with kitchen string.

Remove the rabbit from the pan and add the onions. Stir, season with salt and pepper and cook, stirring and scraping the bottom of the pan to release the browned cooking juices on the bottom of the pan as the onions begin to give up their liquid, until the onions are translucent and tender, 10 to 12 minutes. Return the rabbit and any juices it has given up to the pan, stir, then pour in all the wine and the water. Scrape up any remaining juices from the bottom of the pan. Add the herbs and the plums, pushing them down into the liquid,. Bring the liquid to boil, reduce the heat so the liquid is at a lively simmer and cook, covered,, until the rabbit is cooked through, about 35 minutes, turning the pieces at least twice during the cooking time.

Remove the rabbit from the pan. Increase the heat under the pan so the cooking juices are boiling, and reduce the cooking juices until they are quite thick, which will take 8 to 10 minutes. Return the rabbit to the sauce with any juices it has given up. Turn each piece of rabbit so it is coated with sauce and warm through, which will just take a matter of minutes.

To serve, remove the herbs from the pan, adjust the seasoning, and transfer the rabbit and the sauce to a shallow serving dish. Spoon the sauce over all, and garnish with the fresh herbs. Serve immediately.