Heat 2 tbsp olive oil under moderate-low heat and sautee garlic, then shallots until translucent, about 3 minutes. Add ½ tbsp butter and under moderate heat, sautee mushrooms and leaves from thyme sprigs until mushrooms are soft, about 5 minutes. Add diced sweet potato and sautee another 2-3 minutes. Take out one third of the mushroom/sweet potato mixture and reserve to add later.
Under moderate-high heat, add remaining 1 tbsp olive oil to pan, then add Carnaroli rice and stir to coat every grain of rice, about 1 minute. Add the wine and stir until it is absorbed. Add the heated broth gradually, about ½ cup at a time, stirring continuously to combine with the rice, and only adding more when the liquid has been absorbed. Total cooking time should be 15-20 minutes.
Add 1 tbsp of the parley, and the remaining ½ tbsp butter and fold into the rice. Season to taste with salt and pepper.
Plate into bowls, top with reserved mushroom and sweet potato, them add grated Parmesean cheese and parsley.