Heat a small pot over medium heat. Add 1 tsp. olive oil to hot pot, then add carrots, shallots, and ¼ tsp. salt. Cook, while stirring regularly, 3 minutes or until vegetables begin to soften. Add rice and chicken base and stir 1 minute. Add 1 cup water and butter, then bring to a boil. Reduce heat to low, cover, and cook 15-18 minutes, or until rice has absorbed all the liquid. Fluff with a fork, then stir in black-eyed peas. Cover and cook undisturbed for 2 minutes. Remove from heat and set aside to keep warm.