Place sweet potato in the microwave for 2 minute increments until it is cooked through and you can easily poke a fork through it. Remove skin and add a food processor (or blender) with butter and paprika. Puree until smooth and set aside.
Heat oil in heavy saucepan over medium heat. Add onion and garlic and sauté until the onion is softened, about 3-4 min. Add rice and stir until each grain is coated and toast briefly, about 2 min. Add wine and stir until absorbed.
Add chicken stock a cup or so at a time. Wait until the liquid is absorbed between each before adding more. Once the rice is tender yet still slightly firm in center and looks creamy, about 20 min, stir in sweet potato puree and cheese. Stir until combined and cheese is melted. Season to taste with salt and pepper. Serve immediately.