Sautee the white portions of the scallions until tender, reserve the green portions.
Add pasta and stir frequently until some of the grains are toasted golden brown.
Add 1 cup of the chicken broth, and allow it to absorb, stirring frequently. When it's almost dry, add another 1/2 cup of broth. Continue in this fashion until the pasta is al dente. If you need more liquid, just add a bit more water.
Add chicken, herbs, rest of scallion, Greek seasoning, and juice from half the lemon, stirring until the chicken is warmed through and the herbs have wilted a bit.
The orzo should be soft, and a thick, almost creamy sauce should have developed. At this point, add the myzithra cheese and stir until it's thoroughly incorporated.
Add additional salt, pepper, and lemon juice to correct the seasoning.