Put the sliced cucumbers in a large bowl, sprinkle them with the salt, then set them aside for 30 minutes. Spread the cucumbers out on a double layer of paper towels, pat them dry, then put them back in the dried bowl.
Whisk together the vinegar, olive oil, mustard, and sugar in a small bowl, then pour the dressing over the cucumbers and toss until the slices are evenly coated. Cover the mixture and place it in the refrigerator.
Prepare the grill for cooking. As the coals are heating, halve each tomato and scoop out the seeds. Slice a bit from the rounded end of each tomato half, so that it can sit flat. Brush the tomatoes with olive oil.
Over the hottest coals, grill the tomatoes until they're lightly charred, about 60 to 90 seconds per side, turning once. Transfer the tomatoes to a plate to cool.
Coarsely chop the tomatoes into large chunks, then add them to the cucumbers, along with the onion, parsley, and pepper. Toss the ingredients to blend them evenly. Transfer the salad to a serving dish and top it generously with the feta.