Preheat oven to 350°F. Line an 8x8 inch pan with parchment, leaving overhang for easy lifting.
In a medium bowl, whisk flour, baking soda, and salt; set aside.
In a large bowl, beat softened butter, peanut butter, granulated sugar, and brown sugar until creamy, 1 to 2 minutes.
Beat in the egg and vanilla until smooth and slightly fluffy.
Add dry ingredients to the bowl and mix on low just until combined; do not overmix.
Fold in mini chocolate chips, if using.
Spread dough evenly into the prepared pan. Smooth the top with a spatula.
Bake 20 to 25 minutes, until the edges are set and the top is lightly golden; a toothpick should come out with a few moist crumbs.
Cool completely in the pan, then lift out and cut into 16 bars.
Notes
For neat slices, chill the baked slab for 15 minutes before cutting. Store bars in an airtight container at room temperature for up to 4 days or freeze for up to 2 months.