Preheat the oven to 175 C and line an 8" square baking pan with non-stick (or lightly greased) baking paper, leaving a little overhang for easy removal.
In a microwave-safe mixing bowl, melt the butter, taking care not let it get too hot. If a few lumps remain, stir to melt them completely rather than overheat the mixture.
Add the sugars. Stir very well to combine.
Stir in the vanilla and peanut butter, mixing till combined. I prefer a silicone spatula to stir.
Sift the flour, baking soda and salt into the bowl. Fold gently to make a soft, slightly sticky dough. Finally fold in the chocolate chips, making sure they are evenly dispersed. The dough is quite thick so use some arm muscle here. Stir in the milk one tablespoon at a time to make it easier to mix the dough. You may not need all four tablespoons.
Tip the dough into the prepared pan and press it down firmly and evenly. The dough will look and feel a little greasy because of the melted butter, but it will bake up just fine.
Sprinkle extra chocolate chips on top and drizzle a tablespoon of peanut butter as well, for extra flavour. Bake for 20 to 25 minutes until browned on top. The bars will firm up as they cool so don't worry if they seem a little puffy on the top. Over baking them will make them drier, though if you prefer them that way, go for it!
Allow the bars to cool completely in the pan before lifting them out using the paper overhang and slicing into 16 pieces with a long, sharp knife. Because they are quite soft and gooey, I prefer to store them in the fridge in an airtight container. They will keep for a week to 10 days. Happy baking!