Heat 1 tbsp. oil and 1 tbsp. butter over medium heat in a medium heavy-bottomed pot; add carrots and stir with a wooden spoon until well coated. Add 1/2 cup water, 1/2 tsp. salt, and the sugar; cover and cook 5 minutes, or until tender. Uncover and cook, stirring occasionally, until water evaporates and carrots are just starting to brown, a few minutes more. Reserve half of the carrots. In a blender, purée other half with 3/4 cup hot water.
Bring chicken broth to a simmer and keep at a simmer, covered, over low heat.
Heat remaining oil and butter over medium heat in same (unwashed) pot used for carrots. Add onion and cook until translucent, about 3 minutes. Add rice, stirring with a wooden spoon to coat rice with oil, 1 minute. Add wine and cook, stirring, until wine evaporates. Add carrot purée and cook, stirring, until mixture no longer looks soupy.
Add 1/2 cup hot broth, stirring often, until rice absorbs most of the liquid. Repeat process, adding 1/2 cup broth at a time and stirring often till each addition is absorbed before adding the next, until rice is al dente (about 20 minutes; at least 1 cup broth will remain).
Fold in reserved carrots (save 2 tbsp. for garnish), mascarpone, 1/4 cup parmesan, 1 tbsp. parsley, and the thyme. Add up to 1 cup broth (1/4 cup at a time) to loosen the risotto. Season with salt and white pepper to taste.
Sprinkle each bowl of risotto with some of remaining 1/2 cup parmesan, remaining 1 tbsp. parsley, and reserved carrots. Serve immediately.
Note: Nutritional analysis is per serving.