Toss the tomatoes, sugar, and a portion of the salt together in a bowl and let them sit for 30 minutes to release their juices. Transfer the tomatoes to a salad spinner and spin for 45 to 60 seconds to remove the seeds and excess liquid, stopping to redistribute the tomatoes several times. Return the tomatoes to the bowl and strain the tomato liquid through a fine-mesh strainer into a measuring cup, reserving a half-cup and discarding the rest.

Bring the reserved tomato liquid, shallot, garlic, vinegar, and oregano to a simmer in a small saucepan over medium heat. Cook until the liquid has reduced to about 3 tablespoons, which should take 6 to 8 minutes, then transfer to a small bowl to cool for 5 minutes. Whisking constantly, slowly drizzle in the oil until the dressing is emulsified, then season with salt and pepper to taste.

Add the cucumber, olives, feta, and parsley to the bowl with the tomatoes. Drizzle the dressing over the top and toss gently until the ingredients are evenly coated. Serve immediately while the vegetables are cold and crisp.