Toss the cherry tomatoes with the sugar and salt in a bowl and let the mixture stand for 30 minutes to draw out the juice.

Transfer the tomatoes to a salad spinner and spin until the seeds and juice are separated from the flesh. Strain the collected liquid through a fine-mesh strainer into a small saucepan, discarding the seeds, and place the tomato flesh in a large bowl.

Add the shallot, garlic, vinegar, and oregano to the saucepan with the tomato liquid and simmer over medium-high heat. Cook until the liquid is reduced to about 3 tablespoons, which should take 3 to 5 minutes.

Whisk the olive oil into the reduced tomato mixture and let it cool completely to room temperature before dressing the vegetables.

Add the cucumber, olives, feta, and parsley to the bowl with the tomatoes. Pour the cooled dressing over the top and toss gently until well coated.

Season with salt and pepper to taste and serve immediately while the vegetables are crisp.