Wash carrots and radishes well and pat dry.
Using a mandoline, thinly slice the vegetables into rounds of uniform thickness.
Sprinkle slices with 1 teaspoon salt and 2 teaspoons granulated sugar. Toss to combine and let sit in a cool place for one hour.
When the time is up, pour vegetable slices into a colander and rinse under cold water. Set aside.
In a medium saucepan, combine rice wine vinegar, water, honey, and salt. Bring to a boil.
Once the brine boils, add veg. Stir and cook just until the brine returns to a simmer.
Funnel pickles into prepared jars and apply lids. Let cool.
When pickles are at room temperature, place in the fridge. Let them sit for at least 24 hours before eating.