I’m sure this isn’t unique to my mother. It’s really a kind of quick pickle (say that three times real fast) and probably versions of this go back to antiquity. It’s very easy and makes a refreshing salad on a hot day, and is good the second and third days too.
First, make the dressing/pickling brine:
Make a simple syrup: mix 1/2 cup water and 1/2 cup sugar in a small pan. Bring to a boil to dissolve the sugar, then let cool. (Alternatively, stir sugar and water together like crazy to dissolve sugar.) Add 1/4 cup vinegar (I like apple cider vinegar for this, but use whatever you like) and 1/2 cup water, stir, and taste. You should have a definite sharp sweet-sour taste; if not, add more vinegar/water/sugar as needed. When it’s to your taste, pour into a serving bowl.
Now add vegetables of your choice. Peeled and sliced cucumbers, of course, but also consider sliced onion, bell peppers, green beans, asparagus, summer squash, thinly sliced cabbage, carrots… whatever you like. Add a hot pepper if you want a spicy salad. Toss veggies in the dressing, then put bowl in the refrigerator until ready to serve. I like to make this at least a couple of hours in advance to let the brine soak in.