Preheat your oven to 350°F (175°C) and line a 9x13 inch baking pan with parchment paper, leaving some overhang for easy removal later.
In a large mixing bowl, whisk together the melted unsalted butter, light brown sugar, and creamy peanut butter until well combined. Add in the egg and vanilla extract, mixing until smooth.
Gradually fold in the all-purpose flour and a pinch of salt until just combined. Be careful not to overmix to keep the bars fluffy and tender.
Gently fold in 3/4 cup of the peanut butter chips into the batter, ensuring they are evenly distributed.
Spread the cookie batter evenly into your prepared baking pan. Bake in the preheated oven for about 20-25 minutes, or until the edges are lightly golden and a toothpick inserted in the center comes out clean.
While the cookie base is baking, melt the remaining 1 cup of peanut butter chips in a microwave-safe bowl. Heat in 30-second intervals, stirring in between, until fully melted and smooth.
Once the cookie base is out of the oven and slightly cooled, drizzle the melted peanut butter over the top. Then, pour half of the sweetened condensed milk evenly over the melted peanut butter layer.
Return the pan to the oven and bake for an additional 10-15 minutes, until the sweetened condensed milk has set and the top is lightly golden.
Allow the bars to cool in the pan for at least 30 minutes before lifting them out using the parchment paper. Slice into squares and enjoy your Peanut Butter Sandwich Cookie Bars!