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Season the Chicken: Begin by evenly rubbing the chicken breasts with 1/2 teaspoon of salt and the ground black pepper to enhance flavor.
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Brown the Chicken: Heat a 12-inch skillet over medium-high heat and melt the butter. Once hot, add the seasoned chicken breasts to the skillet. Cook the chicken for approximately 3 to 4 minutes on each side, or until each side is well-browned. Remove the chicken from the skillet and set aside on a plate.
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Prepare the Aromatic Base: Reduce the heat to medium and add the chopped shallot and minced garlic to the remaining butter in the skillet. Sauté for 1 to 2 minutes, or until the shallot and garlic are softened and aromatic.
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Deglaze and Simmer: Pour in the dry white wine to deglaze the pan, scraping up any browned bits from the bottom. Stir in the Dijon mustard and honey, and bring the mixture to a gentle simmer. Add 1 teaspoon of the chopped rosemary, then return the browned chicken to the skillet.
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Cook the Chicken: Lower the heat to medium-low and cover the skillet. Let the chicken simmer for 8 to 12 minutes, or until it is fully cooked and the internal temperature reaches at least 165°F at the thickest part.
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Finish the Sauce: Remove the skillet from the heat. Stir in the whole milk yogurt to incorporate smoothly into the sauce, avoiding curdling. Spoon the creamy sauce generously over the chicken.
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Garnish and Serve: Transfer the chicken to a serving platter and garnish with the remaining teaspoon of chopped rosemary. Serve immediately while hot, ensuring a flavorful and elegant presentation.
