Grease a 9-inch square baking dish with cooking spray.
Melt butter in a saucepan over medium heat. Stir in brown sugar and vanilla extract. Add oats and cook over low heat until combined, 2 to 3 minutes. Spread 1/2 of the oat mixture into the prepared pan.
Melt chocolate chips with peanut butter in small heavy saucepan over low heat, stirring frequently until smooth, about 4 minutes. Pour chocolate mixture over oat layer and spread evenly. Crumble remaining oat mixture over chocolate, pressing in gently.
Cover with plastic wrap and chill until set, 2 to 3 hours or overnight. Bring to room temperature before cutting into bars.