Bring a large pot of salted water to a boil. Cook the pasta until al dente,1-2 minutes less than the package directions. Reserve about 1/4 cup of the cooking water, then drain the pasta and set aside to cool slightly.
Meanwhile, in a large skillet over medium heat, combine the olive oil, tomatoes, and 1/2 teaspoon salt. Cover and cook, stirring occasionally, until most of the tomatoes have burst and released some of their juices, and the oil looks glossy and reddish, 5-7 minutes.
Remove the skillet from the heat. Add the warm pasta to the tomatoes and toss gently to coat, adding a splash of reserved pasta water if the mixture seems dry. Let cool until the pasta is just warm to the touch, 5-10 minutes. It should no longer be hot before you add the cheese.
Stir in the mozzarella pearls and basil. Drizzle with the balsamic vinegar and toss gently to combine, being careful not to break up the tomatoes too much. Taste and adjust, adding more vinegar and salt as needed.
Let the salad rest at room temperature for about 20 minutes to allow the flavors to meld.
Serve slightly warm or at room temperature, or cover and refrigerate until chilled. If chilled, let sit at room temperature for 10-15 minutes and taste again, adding a little extra olive oil, vinegar, or salt just before serving.