It would be easier to produce a Brahma that lays green eggs, instead of one that lays blue eggs, but either one can be done.
Plan on several generations of chickens for the green egg version, so a multi-year project.
And you should plan to eat a lot of chicken meat along the way, because you will produce quite a few birds that are not what you want.
There is one gene that determines whether a chicken lays a blue egg or a not-blue egg. (Brahmas have not-blue).
But there are other genes that determine whether an eggshell has a brown coating on the outside (Brahma eggs) or not (white eggs, blue eggs.)
When the brown coating is on a blue egg, it looks green.
So to get a "Brahma" that lays green eggs, you just have to transfer the blue egg gene into Brahmas. But to get a "Brahma" that lays blue eggs, you also have to transfer the not-brown genes, and that is a lot more difficult, partly because there are a number of them and it's not so obvious how they work.
To get green-egg Brahmas:
Cross the two breeds.
Raise several females, and when they start laying eggs, select ones that lay blue or green eggs. (In this generation, that might be all of them, or it might not be.)
Cross those females to a Brahma rooster.
Then:
a) Raise a bunch of females, and choose the ones that look most like a Brahma, and that also lay blue or green eggs.
b) Cross those females to a Brahma rooster.
Repeat steps a & b until you've got the chickens you want.
If you just keep crossing the green-layers to a Brahma rooster, you will get about half brown-layers and half green-layers in each generation, which might be a nice mix for a backyard flock.
If you want them to breed true for the blue-egg gene (green eggs), that takes some extra steps that are a bit different, done over the next few years.
