Combine 1 1/3 cups stock with turmeric and salt in heavy 2-quart saucepan and bring to boil over high heat.
Add rice, reduce heat to low, cover and cook until liquid is absorbed, about 25 minutes.
Remove from heat and fluff with fork. Cover and keep warm.
Melt butter in heavy large skillet over low heat.
Add onion, cover and cook until softened, about 10 minutes, stirring occasionally.
Add in carrots, increase heat to medium-low and cook uncovered 5 minutes.
Add marjoram and oregano and cook 5 minutes, stirring frequently.
Stir in vinegar, sugar and cinnamon and cook a few minutes to blend flavors.
Add 1/2 cup stock and simmer gently until carrots are crisp-tender and liquid is evaporated, about 20 minutes.
Stir carrots into rice. (Can be prepared 2 days ahead to this point and refrigerated. To reheat, turn into buttered baking dish, cover with foil and bake in preheated 325°F oven until hot, about 30 minutes.)