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Preheat oven to 400 degrees.
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In a large saucepan, bring the broth, water, butter, salt, and pepper to a boil. Add the orzo, stir well, and remove from heat.
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Stir in the chicken, lemon juice, dill, and feta. Stir to combine, then pour into a casserole dish and bake for 20 minutes, until the liquid is mostly absorbed (it'll be a bit sloshy still, but will firm up as it cools).
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Top with Parmesan cheese and let stand for about 5 minutes before serving.