Preheat oven to 350°F. Line a standard muffin tin with paper liners.
Place chocolate and butter in a large microwave-safe bowl and microwave in 30-second bursts, stirring between each burst, until melted and smooth. Let cool slightly.
Whisk in sugar and salt until smooth. Whisk in eggs. Gently whisk in flour and cocoa until just smooth.
Spoon 1 tablespoon of batter into each lined cup. Press 1 peppermint patty on top of batter. Top with 2 more tablespoons of batter, covering peppermint patty completely. Bake, rotating tin halfway through, until a cake tester inserted halfway into the centers comes out with only a few moist crumbs attached, about 25 to 30 minutes. Transfer tin to a wire rack to cool completely before removing cupcakes.
Cupcakes can be stored at room temperature in an airtight container for up to 3 days.