Bring a large pot of salted water to a boil. Add the pasta and cook, stirring occasionally, until tender but still firm to the bite, 8 to 10 minutes. Reserve 3/4 cup of the cooking liquid, then drain the pasta.
Meanwhile, heat the olive oil in a large, high-sided skillet over medium heat. Add the garlic and cook until lightly browned, about 2 minutes. Remove the garlic and discard. Add the spinach and 2 teaspoons pepper, and cook until the spinach has wilted, about 1 minute.
Remove the skillet from the heat and add the pasta. Add the Pecorino Romano cheese and 2 teaspoons each salt and pepper, and toss until coated.
In a medium bowl, whisk together the reserved cooking liquid and the mascarpone cheese until smooth. Pour over the pasta and toss until coated. Season with salt.
Transfer the pasta to a large bowl and serve.