Step 1: Preheat your oven to 350°F (175°C). Line a 9×13 inch baking pan with parchment paper, leaving an overhang on the sides for easy removal. Lightly grease the parchment paper.
Step 2: In a large mixing bowl, cream together the softened butter and granulated sugar with an electric mixer until light and fluffy, about 2-3 minutes. Scrape down the sides of the bowl.
Step 3: Add the creamy peanut butter to the butter-sugar mixture and beat until well combined. Then, add the eggs one at a time, beating well after each addition, until the mixture is smooth.
Step 4: In a separate medium bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix; the dough will be thick.
Step 5: Transfer about two-thirds of the cookie dough to the prepared baking pan. Using lightly floured hands or a greased spatula, press the dough evenly into the bottom of the pan to form a compact base.
Step 6: Evenly pour the entire can of sweetened condensed milk over the peanut butter cookie dough base.
Step 7: Crumble the remaining one-third of the cookie dough over the layer of sweetened condensed milk.
Step 8: Bake for 30-35 minutes, or until the edges are golden brown and the top is lightly golden. The center may still appear soft.
Step 9: Remove from oven and let the bars cool completely in the pan on a wire rack for at least 2-3 hours, or chill in the refrigerator for 1-2 hours, before lifting out by the parchment paper handles and cutting into squares. This allows the gooey center to set. Store in an airtight container.