Using a mandoline or sharp chef’s knife, thinly slice cucumber and radishes. In a small bowl, combine the vinegar, sugar and 1/4 teaspoon salt, stirring until the sugar and salt are dissolved. Add the cucumber and cilantro and toss to combine. Let sit, tossing occasionally, for at least 15 minutes and up to 6 hours.
Meanwhile, heat a drizzle of oil in a pan. Sprinkle the meat with salt and pepper and gently mix it by hand without breaking it up too much. Form loosely into patties.
Place the patties in the pan – it should be hot enough that they sizzle. At no point should you squash the burger – keep the juices inside! Cook until the first side is well browned, then flip. Remove from pan when they are done to your liking.
Toast buns and assemble your burgers with quick pickles, a lettuce leaf, a tomato slice and your favorite burger accompaniments.