Place a carrot onto a flat work surface. Working lengthwise and with firm pressure, use the peeler to slice the carrot into long, thin ribbons. Repeat this process with all carrots. Place the carrot ribbons into a 1-pint/480ml mason jar. Add the mustard seeds, if using.
Combine the water, vinegar, sugar and salt in a heatproof liquid measuring cup. Pour this mixture into a small saucepan and bring to a simmer over medium low heat, or microwave the mixture for 2 1/2 minutes. .
Pour the hot pickling liquid over the ribbons in the jar. Submerge them completely.
Allow the ribbons to sit at room temperature for 20-30 minutes. Use right away, or cover the jar tightly with a lid and store in the fridge for 2 weeks.