Mix brine ingredients in the bottom of a medium bowl and set aside. Prepare your vegetables: Trim and core cabbage and slice thinly with a knife, food processor slicing blade or adjustable-blade slicer. Place in a large bowl. Core, seed and thinly slice red pepper; peel and thinly slice or julienne carrot; thinly slice cucumber (I quartered mine first). Add vegetables to cabbage bowl.

By the time you’re done preparing your vegetables, the sugar and salt in the pickling mixture should have dissolved. If not, whisk a few times until they do. Taste and adjust if you’d like it a little saltier — I added 1 more teaspoon of kosher salt in the end. Pour pickling brine over vegetables and cover bowl with a lid or plastic wrap. Refrigerate for 1 hour or up to 1 week. Salad becomes more pickled as it rests. Eat with everything.