Meanwhile heat olive oil in a large skillet over medium heat. Add shallots; cook and stir until shallots begin to soften, about 1 minute. Add tomatoes and kale; cook and stir until most of the liquid from the tomatoes has evaporated and kale is tender.
Drain pasta and add directly into tomato mixture; stir to combine. Season to taste with salt and freshly ground black pepper.
Divide pasta mixture into two serving bowls and drizzle with olive oil. Divide mozzarella evenly over bowls and serve.