Place a saucepan with a tight fitting lid over medium heat. Add the olive oil and heat for 2 minute. Add the pecans and toast, stirring with a wooden spoon, until the nuts are fragrent, about 1 minute. Add the rice and toast for 2 minutes, stirring frequently. Add the shallots, carrot, salt and pepper.

Cook the rice and vegetables for an additional 3 minutes. Add the stock, increase the heat to high and bring the mixture to a simmer. Decrease the heat to low, cover and cook for 12 minutes. Remove from the heat and let the rice sit, covered, for another 10 minutes.

Stir in the green onions before serving.