Place lamb shanks in a 7 by 11 inch baking dish with meaty portions to outside of dish.
Distribute onion and green pepper slices over and around shanks.
In a small bowl, stir together tomato juice, wine, garlic, thyme, savory, and pepper; pour over shanks.
Cover with pleated plastic wrap.
Microwave on medium (50%) for 1 1/4 hours or until shanks are fork tender.
With a slotted spoon, transfer shanks to a rimmed serving platter and top with vegetables.
Skim off and discard fat from juices in dish.
Stir together cornstarch and water.
With a wire whip, blend into juices along with salt to taste.
Microwave, uncovered, on HIGH (100%) for 4 minutes (stirring after 2 minutes) or until sauce thickens.
Pour over shanks.