In a heavy ovenproof kettle large enough to hold veal shanks in one layer heat 1 tablespoon each of olive oil and butter over moderately high heat until foam begins to subside and saute onion and celery until beginning to turn golden.
Pat shanks dry between paper towels and season with salt and pepper. Arrange shanks on onion mixture and roast, covered tightly, in middle of oven 3 hours. (Meat will give off juices as it cooks.) Shanks may be prepared up to this point 1 day ahead and cooled, uncovered, before chilling, covered. Reheat shanks before proceeding.)
Cut mushrooms into 1/4-inch-thick slices. in a large skillet heat remaining 2 tablespoons each of olive oil and butter over moderately high heat until foam begins to subside and saute mushrooms with thyme and salt and pepper to taste, stirring, until mushrooms begin to give off their liquid.
Stir in vermouth or wine and lemon juice and cook, stirring, until all but about 1/3 cup liquid is evaporated. Mushrooms may be made 1 day ahead and cooled completely before chilling, covered.
Transfer shanks to a platter and keep warm.
Transfer onions, celery, and pan juices to a blender with 1/2 cup water and puree until smooth, adding more water if necessary to thin sauce to desired consistency.
Pour sauce into a saucepan and stir in mushroom mixture, vinegar, and salt and pepper to taste. Heat sauce over moderate heat until heated through and stir in parsley.
Arrange shanks on couscous and spoon sauce over them.