An EE is a chicken that (hopefully) has the gene for blue eggs. Green eggs are produced toward the end of the laying process when a brown coat is added over the blue to make green. (If you check the inside of the green egg shell it will be blue.) Brown eggs are actually white shells with a brown coat. (Check inside to see white.)
Your EE has some brown layer ancestry to make the those green eggs and that is the color she will continue to make. I have heard of an older hen losing the "coating" process due to age or stress, which will result in the same hen laying two different colored eggs, but usually it's the same color for the life of the hen.
The hatcheries are claiming that EEs as a "breed" can lay different colored eggs, but you have to have different hens!
Love those EEs!