In a saucepan over medium heat, heat all ingredients (except for radishes), stirring until the sugar dissolves. Remove from heat and let cool. Strain into a large jar over thinly sliced radishes and store in the fridge until planned use. They'll last for a while in a tightly-sealed container.
Chilled Avocado, Yogurt, and Charred Serrano Soup
Add the avocado, yogurt, cucumber, and lime juice and zest to a blender or food processor and purée. Add water as needed to achieve the desired thickness of the soup.
Pour the puree into a bowl and fold in most of the charred serranos and scallions, and season with salt and pepper to taste.
Garnish with pickled radishes and the extra scallions and serranos. Serve immediately.