Begin by washing your carrots, cucumber, and radish under cold water to remove any dirt. Slice carrots and cucumber into thin matchsticks using a sharp knife or a cheese grater for quicker prep. Cut radishes the same way. Aim for uniform thickness to ensure even pickling. Once prepped, set your vibrant vegetable mix aside, ready to soak up those tangy flavors.

In a medium saucepan, combine equal parts water and vinegar, then bring the mixture to a boil over medium heat. Stir in chopped green onion, minced garlic, sea salt, dried oregano, and sugar, mixing until completely dissolved—this usually takes about 2-3 minutes. Once the brine is bubbling and fragrant, remove it from heat and let it cool for 5-10 minutes, allowing the flavors to meld beautifully.

Grab a clean mason jar, and begin layering your prepared vegetables inside. For a visually appealing presentation, alternate layers of carrots, cucumber, and radish. Once the jar is packed with colorful veggies, slowly pour the cooled vinegar brine over them, ensuring all vegetables are submerged.

Allow the filled jar to sit at room temperature for about 10 minutes, letting the brine soak into the vegetables. Once cooled, securely cover the jar with a lid and transfer it to the refrigerator. For optimal flavor and crunch, strive to enjoy your pickled vegetables within the same day, though they’ll last well for up to two weeks in the fridge.