Heat ¼ cup of olive oil in a large pot to medium heat. Once the oil is hot add the onions and cook for 1 minute.
Add the carrots, jalapeños, and radishes and let cook for 1- 2 minutes. Add the vinegar to the hot pot with the vegetables. (Be careful. When the vinegar touches the oil there will be some splashing.)
Add the water, thyme, oregano, bay leaf, and salt. Let simmer for 8- 10 minutes or until the vegetables are tender, but not completely soft.
While the vegetables are cooking, sterilize your jars by boiling them in water for 5 min. When your vegetables are ready, use canning tongs to remove the jars from the water, pouring the water in the jars back in the canner.
Bring the water in your canning pot back to a boil. Pour the vegetables into the jars using a ladle and a canning funnel, but be sure to leave ½ inch of headspace at the top.
Use a chopstick to release air bubbles by running it around the inside of the jar. Clean the rims of the jars with a moist paper towel. Put on the lids and screw the rings on until finger tight. Do not force it.
Transfer the jars to the pot, making sure they are vertical and that there is at least one inch of water covering them. Bring water to a boil and process cans for 10 minutes.
Remove jars from water and place on top of a wire rack. Let cool. You should hear a pop when the lids seal completely. Leave undisturbed for 6 hrs. If the lids are not sealed properly you will have to process them again.
Remove the rings and store jars in a cool, dark place. Refrigerate after opening.