Wash the jalapeños and carrot thoroughly. Slice the jalapeños into thin rounds or leave them whole, making a small slit in each to help the brine penetrate. Slice the carrot into thin rounds. Lightly smash the garlic cloves.
Make the Pickling Brine
In a small saucepan, combine the water, white vinegar, apple cider vinegar, kosher salt, sugar, and mustard seeds. Heat over medium-high heat, stirring occasionally until the salt and sugar dissolve completely.
Pack the Jars
Divide the sliced jalapeños, carrots, and garlic evenly between clean glass jars, leaving a little space at the top.
Pour the Hot Brine
Carefully pour the hot brine over the jalapeños, carrots, and garlic in the jars, ensuring everything is fully submerged.
Seal and Cool
Place the lids on the jars, but don’t tighten them too much. Let the jars cool at room temperature for about 30 minutes.
Refrigerate
Once cooled, tighten the lids and store the jars in the refrigerator. Allow the pickled vegetables to sit for at least 24 hours to develop flavor.
Notes
Let the pickled mix sit for 2–3 days for the best flavor.