Season the Chicken: Begin by evenly rubbing the chicken breasts with 1/2 teaspoon of salt and the ground black pepper to enhance flavor.
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.
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.
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.
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.
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.
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.