Preheat an oven to 400 degrees F (200 degrees C). Butter a baking dish.
Whisk the sour cream, Dijon mustard, garlic, and pepper together in a large bowl. Add the chicken and turn to assure the breasts are well coated. Refrigerate 20 to 30 minutes.
Combine the cornflakes and onion soup mix in a bowl. Gently press the chicken breasts into the cornflakes mixture to coat and shake off any excess. Lie the coated breasts in the buttered baking dish. Drizzle the melted butter over the chicken.
Bake in the preheated oven until the chicken is golden brown, 20 to 25 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).