In a large stainless-steel, enamel, or nonstick saucepan combine mushrooms and lemon juice. Add enough water to cover; bring to boiling. Boil for 1 minute; drain.
In a medium stainless-steel, enamel, or nonstick saucepan combine balsamic vinegar, wine vinegar, honey, rosemary, peppercorns, salt, and garlic. Bring mixture to boiling, stirring to dissolve honey; reduce heat. Simmer, covered, for 10 minutes. Remove from heat; stir in shallots.
Pack mushrooms into hot sterilized half-pint canning jars, leaving a 1/2-inch headspace. Pour hot vinegar mixture over mushrooms, distributing the rosemary, peppercorns, and garlic evenly among jars and maintaining the 1/2-inch headspace. Wipe jar rims; adjust lids and screw bands.
Process filled jars in a boiling-water canner for 20 minutes (start timing when water returns to boiling). Remove jars from canner; cool on wire racks. Makes 5 half-pints.