Preheat oven. Place tomatoes cut side up on a rimmed baking sheet. Drizzle with olive oil and Kosher salt. Cook, rotating the pan once halfway through cook time, until blistered and juicy.
Meanwhile, bring a large pot of salted water to a boil. Add spaghetti and cook according to package directions for al dente. Before draining reserve about pasta cooking liquid in a measuring cup. Drain pasta. Toss pasta with unsalted butter or olive oil to ensure it doesn't stick.
Add cooked tomatoes, rotisserie chicken, pesto, mascarpone cheese, lemon zest, and reserved cooking water, then toss to combine. Mascarpone should be completely melted.
Add bocconcini or ripped mozzarella and fresh arugula, then toss once more. Sprinkled with flaky sea salt and lots of freshly cracked black pepper. Serve immediately.