Line an 8-inch or 9-inch square baking dish with parchment paper and set aside. Overhangs the edges of the foil to lift the bars easier from the baking dish. (You can use a 9x13-inch if you want thinner bars.)
Melt butter and brown sugar in a large saucepan over medium heat, until the butter has melted and the sugar has dissolved. Stir in vanilla. Mix in the oats.
Cook over low heat for 3 to 4 minutes, or until ingredients are well blended.
Pour half of the oat mixture into the prepared baking dish. Spread out the mixture evenly, pressing down. Reserve the other half for the second layer.
To make the filling, melt the peanut butter and chocolate chunks together in a small microwave-safe bowl and stir until it’s smooth.
Pour the chocolate mixture over the crust in the pan, reserving about 1/4 cup for drizzling and spread evenly.
Pour the remaining oat mixture over the chocolate layer, pressing in gently and drizzle with the remaining chocolate mixture.
Refrigerate 2 to 3 hours or overnight. Bring to room temperature before cutting into bars.
Note: Like any no-bake cookie, the final texture of these really depends on how long you boil the sugar mixture. If it doesn't boil long enough, the cookie/bars mixture will be too soft, if you boil too long, they could turn out dry and crumbly.