Heat the oil in a large saucepan over medium-high heat; cook the corn kernels in the hot oil until tender, about 5 minutes. Stir the poblano pepper, onion, peas, garlic, and carrot into the corn; cook and stir another 5 minutes.
Pour the water and milk into the mixture; bring to a boil. Allow the butter to melt into the boiling mixture. Add the rice and stir. Season with chicken bouillon; cover the saucepan, reduce heat to medium-low, and simmer the mixture until all the liquid is absorbed and the rice is tender, about 20 minutes.