Salt the tomatoes. Halve the tomatoes lengthwise and place the tomatoes cut side up on a plate or cutting board. Season with 1/2 teaspoon Kosher salt. Set aside while you make the vinaigrette.
Make the Italian vinaigrette. Add the olive oil, red wine vinegar, grated garlic, oregano, salt and ground pepper (if using) to a glass jar. Cap the jar with a tight-fitting lid and shake until the dressing is creamy and emulsified, about 1 minute. Alternatively, you can use a bowl with a whisk to make the dressing.
Assemble the salad. In a large bowl, combine the salted tomatoes, leaving any juices behind, diced cucumbers, and mozzarella cheese.
For serving. Shake the salad dressing right before serving. Drizzle the dressing over the salad and coat to taste. Store extra dressing in an airtight container in the refrigerator for up to 5 days. If the dressing solidifies in the refrigerator, set aside at room temperature until the olive oil liquifies, about 5 minutes.