Bring a large pot of water to a boil. Add the pasta and cook it until al dente. Strain the pasta and transfer it to a large bowl to cool slightly. Toss in 1 tsp olive oil. While the pasta cools, make the dressing.
In a small bowl, whisk together all of the dressing ingredients, except for the olive oil. While whisking, stream in the olive oil. Season the dressing with salt and pepper, to taste.
Add the tomatoes, cucumbers, and mozzarella cheese to the bowl with the pasta.
Pour the dressing over the pasta, tossing to combine, then cover the salad and refrigerate it for at least 3 hours. When ready to serve, toss the pasta salad again and enjoy cold or at room temperature.