In a large shallow skillet, melt the butter and brown the butter over medium high heat.
The butter will foam up and then turn brown. Once the butter is nutty and fragrant, add the orzo and crushed garlic.
Stir the pasta constantly to coat all the orzo. Continue to stir constantly until about half the orzo begins to brown.
Deglaze the pan with the white cooking wine. Once all the wine is evaporated and absorbed, add the chicken broth and reduce the heat.
Cover the skillet with a lid. Simmer until all the liquid is absorbed and is the orzo is tender, stirring occasionally. This will take up to 15-20 minutes, but check after 10.
Add the parsley and the grated mizithra cheese, stirring to incorporate.