In a small bowl, whisk together the red wine vinegar, freshly pressed garlic clove, olive brine, sugar, salt, and dried oregano. Let this mixture sit for 1-2 minutes to allow the garlic and oregano to infuse into the vinegar. Slowly whisk in the extra virgin olive oil until emulsified. Taste and adjust seasoning if needed. This dressing benefits from a few minutes of rest, so you can prepare it while working on the vegetables.
While the dressing infuses, halve the cherry tomatoes and slice the red onion into paper-thin slivers (a mandoline works beautifully here). Pit the kalamata olives if they haven't been already, and tear the fresh basil leaves by hand—this prevents bruising and oxidation better than cutting. Keep the mozzarella pearls separate until the final assembly, as they're best added just before serving to maintain their delicate texture.
Add the halved cherry tomatoes to a large serving bowl. Pour about three-quarters of the vinaigrette over the tomatoes and gently toss to coat—I like to reserve some dressing to drizzle at the end for a more dynamic presentation. Add the sliced red onion and kalamata olives, then gently fold everything together. Add the mozzarella pearls last, folding gently to avoid breaking them.
Top the salad with the torn basil leaves and finish with a generous grind of freshly cracked black pepper. Drizzle with the reserved vinaigrette and, if desired, a small amount of balsamic glaze for added richness. Serve immediately while the mozzarella is still cool and the basil is fragrant.