How to Make It
Trim tops from carrots, leaving 1 inch of greenery on each; peel carrots. Cut carrots in half lengthwise. Bring vinegar, granulated sugar, brown sugar, salt, molasses, mustard seeds, and peppercorns to a boil in a medium-size nonaluminum saucepan over medium-high heat, stirring until sugars and salt dissolve. Reduce heat to medium; add carrots and onions, and simmer 3 minutes, stirring occasionally.
Place broccoli and next 3 ingredients in a large heatproof bowl; pour hot vinegar mixture over vegetables. Cool completely (about 1 hour). Stir occasionally while mixture cools.
Transfer vegetables to 2 hot sterilized 1-qt. jars, using a slotted spoon and filling to 1 inch from top. Pour cooled vinegar mixture from bowl into a liquid measuring cup with a pour spout. Pour enough vinegar mixture into jars to cover vegetables, and discard remaining vinegar mixture. Cover with metal lids, and screw on bands. Let stand 24 hours before using. Refrigerate in an airtight container up to 2 weeks.