For sauce, in a small saucepan, cook chopped onion in butter or margarine until tender, but not brown. Stir in apple cider or juice, vinegar, honey, steak sauce, salt, and pepper. Bring to boiling. Reduce heat; simmer, uncovered, for 20 minutes, stirring occasionally.
Meanwhile, in a large saucepan, add sausages to boiling water. Reduce heat; simmer, covered, for 10 to 15 minutes or until sausages are thoroughly cooked. Drain. Let cool slightly. Meanwhile, start coals for grilling. Cut sausages crosswise into 2-inch pieces.
Cook boiling onions, uncovered, in boiling water for 3 to 5 minutes. Drain.
On four 10-inch skewers, alternately thread sausage pieces, boiling onions, and mushrooms. Grill the kabobs on an uncovered grill directly over medium-hot coals* for 10 to 12 minutes, turning and brushing often with the sauce.
Thread a cherry tomato on the end of each skewer. Return kabobs to grill for 2 to 3 minutes or until tomatoes are heated through. If you like, bring remaining sauce to boiling and serve warm with kabobs. Makes 4 servings.
To test for medium-hot heat, you should be able to hold your hand over the heat at food height for 3 seconds before having to pull away.