Heat oil in a very large skillet or Dutch oven over medium-high heat. Add mushrooms and cook for 10 minutes, stirring occasionally. Stir in shallots, sherry or broth, and garlic and continue cooking, stirring occasionally, until most of the juices have evaporated, 10 to 14 minutes. Stir in lemon juice. Set aside.
In a large saucepan combine water, vinegar, and thyme. Bring mixture to boiling.
Pack 1/2 cup mushroom mixture and 1 cup beans tightly into 9 hot pint canning jars, leaving 1-inch headspace. Sprinkle 1/2 teaspoon salt into each jar. Ladle boiling liquid into hot jars, leaving 1-inch headspace. Remove air bubbles. Wipe rims; adjust lids and screw bands.
Process filled jars in a pressure canner at 11 pounds pressure (dial-gauge canner) or 10 pounds pressure (weighted gauge canner) for 20 minutes, adjusting for altitude. When processing time is complete, allow canner to depressurize. Carefully remove canner lid; let jars cool in canner for 10 minutes. Remove jars from canner and cool on a wire rack. Check lids for seal after 24 hours.
Before using, place contents of jar in a small saucepan. Bring to a rapid boil. Boil, covered, for 10 minutes (add 1 additional minute for each 1000 feet of elevation).
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2 g fat
(0 g saturated fat,
0 g polyunsaturated fat,
1 g monounsaturated fat),
0 mg cholesterol,
593 mg sodium,
13 g carbohydrates,
3 g fiber,
8 g sugar,
3 g protein.