Combine butter, chicken broth, milk, oregano, and salt in a 3-qt sauce pot. Bring to a boil over medium-high heat. Slowly whisk in the grits.
Cover, reduce the heat, and simmer for 8-10 minutes, stirring occasionally. Add cheese, sour cream, sage, and parsley. Whisk to combine and cook until the cheese is melted and the grits have a creamy texture. Serve immediately.
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