Bring a large pot of water to a boil, then add carrots, green beans and 1 tablespoon salt. Bring the water back to a boil, reduce the heat and simmer for 2 minutes.
Drain the vegetables and immediately rinse them with very cold water to stop the cooking.
Place carrots, green beans, radishes and onions decoratively into about five 8-ounce Mason jars (or fewer, larger Mason jars, as you wish).
Add water, vinegar(s), sugar and remaining salt to a saucepan and bring to a boil. Once the sugar has been completely dissolved, carefully pour the hot liquid over the vegetables in the jars. Let cool to room temperature, cover the jars with their screw-top lids and store in the refrigerator.
These are best after at least a day in the vinegar, and will keep for up to 2 weeks.