In a large skillet that has a tightly fitting lid, melt the butter over medium-low heat.
While the butter is melting, put the peas in a colander and run cool water over them until they are thawed. This should only take a few minutes. When the peas are thawed, shake them to drain and set them aside until they are needed.
Add the carrots and saute them for about three minutes or until they are slightly softened. Add the onions and cook them along with the carrots for about five minutes or until they are soft and golden in color, stirring them occasionally.
Add the rice to the pan and stir it until it is coated in the butter and mixed in with the vegetables.
Add the peas and stir the mixture.
Add the broth or the water and salt, stirring the rice. Turn the heat to medium and bring the pan to a boil.
Reduce the heat under the pan to low and put the lid on the pot, completely covering it so that little steam can escape. Simmer the mixture for 15 minutes without stirring.
After 15 minutes the rice should be fully cooked and the liquid is completely absorbed. Sprinkle the rice with the parsley return the cover to the pan. Let the rice standoff from the heat for 5 minutes before you serve it.