Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until the rice is tender and liquid has been absorbed, 20 to 25 minutes.

Preheat the oven to 350 degrees F (175 degrees C).

Pour just enough water into a large skillet to cover the bottom in a shallow layer; add chicken pieces in a single layer. Season chicken with salt and pepper. Turn heat to medium-high and cook chicken until no longer pink in the center and the juices run clear, adding water as needed to keep pan wet, 7 to 10 minutes; drain liquid.

Stir cooked rice, cooked chicken, cream of chicken soup, milk, and Mexican blend cheese together in a casserole dish. Smooth the top of the mixture with the back of a spoon. Arrange biscuit dough over the rice and chicken mixture, breaking dough pieces as needed to get maximum coverage and to avoid overlap.