Preheat your oven to 350°F (175°C) and grease the 9x13 inch baking pan.
In a large mixing bowl, combine the peanut butter, softened butter, granulated sugar, and brown sugar. Mix until creamy and smooth.
Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the peanut butter mixture, mixing until fully incorporated.
Spread the batter evenly into the prepared baking pan.
Bake in the preheated oven for 20-25 minutes, or until the edges are golden brown and a toothpick inserted in the center comes out clean.
Remove the bars from the oven and immediately press the chocolate kisses into the warm bars in a grid pattern, spacing them evenly.
Allow the bars to cool in the pan for about 10 minutes before cutting into squares.