Preheat oven to 350 °F (175 °C). Line two baking sheets with parchment paper.

In a mixing bowl, stir together peanut butter, granulated sugar, brown sugar, egg, vanilla, baking soda, and salt until smooth and well combined.

Scoop dough by tablespoonfuls (about 1 Tbsp each) and roll into balls. Place on prepared baking sheets about 2 inches apart, then gently flatten each with your fingertips or fork to about ½‑inch thickness.

Bake for 8–10 minutes, just until edges are set and tops appear slightly cracked. Do not overbake.

Remove from oven and allow cookies to cool on baking sheets for 5 minutes, then transfer to wire racks to cool completely.

While cookies cool, melt chocolate chips and butter (or oil) in a microwave in 20‑second bursts, stirring until smooth; or melt over a double boiler.

Dip the top half of each cookie into the melted chocolate, letting excess drip off. Return to parchment-lined sheet. If desired, use a toothpick to swirl a little chocolate into a “buckeye” pattern.

Chill cookies in refrigerator for about 15–20 minutes, until chocolate sets completely.

Store cookies in an airtight container in the refrigerator for up to one week, or freeze for longer storage.