1. Trim off bottom of asparagus so that asparagus fits into 2 (1-qt.) sterilized canning jars, leaving 1/2-inch headspace. Discard asparagus ends. Divide salt and next 4 ingredients between jars. Pack trimmed asparagus, pointed ends up, into jars.
2. Bring vinegar, sugar, and 1 cup water to a boil in a small saucepan over medium-high heat. Pour vinegar mixture over asparagus, filling to 1/2 inch from top. (Fill jars with additional hot water, if needed.) Remove air bubbles; wipe jar rims. Cover with metal lids, and screw on bands. Shake to combine, and chill 24 hours. Store in refrigerator up to 1 month.