Place broth in a medium saucepan; bring to a simmer over medium-high heat. Reduce the heat so the broth remains steaming, but is not simmering.
Heat oil in a Dutch oven over medium-low heat. Add onion and cook, stirring occasionally, for 5 minutes. Add garlic and cook, stirring, until the onion is very soft and translucent, about 2 minutes. Add rice and salt and stir to coat.
Stir 1/2 cup of the hot broth and a generous splash of wine into the rice; reduce heat to a gentle simmer and cook, stirring constantly, until the liquid has been absorbed. Add more broth, 1/2 cup at a time along with some wine, stirring after each addition until most of the liquid has been absorbed. After about 10 minutes, stir in tomato paste. Continue to cook, adding broth and wine and stirring after each addition until most of the liquid is absorbed; the risotto is done when you've used all the broth and wine and the rice is creamy and just tender, 20 to 30 minutes more.
Remove the risotto from the heat; stir in 3/4 cup cheese and pepper. Serve sprinkled with the remaining 1/4 cup cheese.