Heat the oven to 350°F. Have the half sheet jelly roll pan, approximately 17.8 x 12.8 x 1 inch, ready before mixing so the dough can go straight into the oven.

Beat the softened butter, sugar, and firmly packed brown sugar in a large bowl until pale and fluffy. The mixture should look lighter in color and lose its grainy, heavy appearance.

Mix in the vanilla extract, eggs, and 1 cup of the peanut butter until fully blended. Stop when the batter looks creamy and uniform, without streaks of egg or peanut butter.

Add the oats, flour, baking soda, and salt, then mix until the dough comes together. The finished dough will be thick and scoopable, with oats distributed throughout.

Coat the baking sheet with nonstick cooking spray and press the dough into an even layer from edge to edge. Level thickness matters because thin spots can brown too quickly while thicker areas remain underbaked.

Bake for 15 minutes, then take the pan out of the oven. Look for pale golden edges while the center still feels slightly soft, which keeps the bars chewy after cooling.

Scatter the remaining peanut butter, about 1 ½ cups, over the warm crust in very small spoonfuls. Let it sit for about 5 to 6 minutes until it softens and develops an even glossy sheen.

Gently spread the softened peanut butter across the crust. Do not force thick peanut butter across the hot base, since it can pull up pieces of the tender crust.

Let the bars cool completely until the peanut butter layer has set. The surface should no longer look loose or runny before the frosting goes on.

Beat the frosting ingredients with a hand mixer until smooth, then spread the frosting over the cooled bars. A fully cooled peanut butter layer keeps the chocolate buttercream thick, neat, and in place.

Cut the pan into bars and serve. For a softer bite, serve at room temperature; chilling creates a firmer peanut butter and frosting layer.