Peel the red onion and cut off the root and stem ends. Slice the onion very thinly across the grain into half-moons (use a sharp knife or mandoline set to about 1.5–2 mm). Place the slices in a medium bowl and add the cold water and 1 tsp kosher salt. Stir gently and let sit for 10 minutes to remove some bite and crisp the texture. After 10 minutes, drain the onions in a fine-mesh sieve and pat lightly with paper towels to remove excess water.

Make the dressing

In a small bowl or jar, combine 3 tbs extra-virgin olive oil, 1 tbs red wine vinegar, 1 tsp fresh lemon juice, 1 tsp granulated sugar, and 1 tsp freshly ground black pepper. Whisk or shake vigorously until the sugar dissolves and the dressing emulsifies. Taste and adjust seasoning — add up to 1/4 tsp more salt if needed. (Note: the 1 tsp kosher salt used to mellow the onions is mostly drained away; final seasoning should be adjusted to taste.)

Assemble the salad

Return the drained onion slices to a clean bowl. Pour the dressing over the onions and toss gently with tongs or a fork until evenly coated. Finely chop the fresh parsley and (if using) the mint; add them to the bowl and toss to combine. If using, crumble the feta over the top and add the lemon zest. Taste and adjust acidity or salt: add another 1/2 tsp red wine vinegar or a pinch of salt if the salad needs brightness.

Rest and serve

Let the salad rest at room temperature for 10–15 minutes so flavors meld (or refrigerate for up to 30 minutes for a cooler salad). Give it one final toss before serving. Serve as a bright condiment with grilled meats, roasted vegetables, sandwiches, or as part of a meze spread. Leftovers keep covered in the refrigerator for up to 2 days; bring to room temperature before serving for best flavor.