To make the dressing, combine all ingredients in a small bowl, adding smashed garlic clove at the end. Let the garlic infuse the dressing as you prepare the rest of the ingredients.
Slice off the ends of each cucumber and discard. Using the broad side of a chef’s knife, smash the cucumbers to flatten, then slice on the bias into 1” pieces. Gently tear the pieces with your fingers and transfer the cucumbers to a colander over a bowl or in the sink. Sprinkle all over with Kosher salt and let the cucumbers sit for ten minutes. Transfer to a clean kitchen towel and pat them dry before placing them in a serving bowl with the minced chile.
Remove the garlic from the dressing and discard. Spoon the dressing generously over the cucumbers and toss. Add the salad toppers and the mint leaves, season with Maldon salt to taste and serve immediately.