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The cheesy filling in this chicken hearkens to the beloved cream cheese and pepper jelly appetizer, but the herbs and garlic give it a bit more flavor depth.
Preheat oven to 375°F. Gather all ingredients.
Combine cream cheese, mozzarella, basil, chives, and garlic in a medium bowl, stirring until well combined. Cut a pocket into each chicken breast by inserting the tip of a chef’s knife in the thickest part of the breast and cutting a horizontal slit 3/4 of the way through the breast. Stuff the cheese mixture evenly into the chicken breasts. Season breasts on both sides with salt and pepper. Secure breasts closed with a toothpick, if desired.
Heat a large cast-iron or other ovenproof skillet over medium-high. Add oil to pan and swirl to coat. Add chicken to pan. Cook until browned, 5 to 6 minutes on each side.
Transfer skillet to oven. Bake chicken at 375°F until cooked through, about 15 minutes.
Remove chicken from pan and place on a platter. Place skillet over medium-high heat. Add broth to pan, scraping pan to loosen browned bits. Whisk in pepper jelly and lemon juice. Cook until mixture is syrupy, 2 to 4 minutes. Remove pan from heat and whisk in butter. Pour glaze over chicken.