Cut carrots lengthwise in ¼" slices; then cut in strips about ¾" wide and 3" long.
Cook garlic and chopped onion in salad oil until almost tender, about 5 minutes (do not let brown).
Stir in vinegar, salt, dry mustard, pepper, pickling spices, tied in a cheesecloth bag, and carrots. Cover and simmer about 5 minutes (carrots should be crunchy and crisp).