In a small measuring cup, combine and stir sunflower oil, distilled white vinegar, fine salt, and pepper until well combined and salt dissolves. Set aside.
Wash all vegetables thoroughly and pat dry with paper towels.
Discard any soft outer leaves from the cabbage. Thinly slice the cabbage using a mandolin slicer or a sharp knife. Discard or eat the core. Transfer the shredded cabbage to a large mixing bowl.
Halve the cucumbers lengthwise, then thinly slice them. A mandolin slicer makes this step quick and easy. Add sliced cucumbers to the bowl with the cabbage.
Finely chop the green onions and fresh dill, then add them to the mixing bowl.
Drizzle the prepared salad dressing over the vegetables in the bowl and toss well to combine all ingredients evenly.
Serve the Green Cabbage Cucumber Salad immediately for maximum crispness, or refrigerate for a couple of hours for the cabbage to soften slightly before serving.