Preheat your oven to 350°F (175°C). Line two or three large baking sheets with parchment paper or silicone baking mats. Set aside.

In a large mixing bowl, use an electric mixer on medium speed to cream together the softened butter, 1 cup of peanut butter, granulated white sugar, and light brown sugar until the mixture is light and fluffy (approximately 2 to 3 minutes). Add the two large eggs, one at a time, mixing well after each addition. Stir in the vanilla extract until fully incorporated. Scrape down the sides of the bowl as needed.

In a separate medium bowl, whisk together the all-purpose flour, baking soda, and salt. Gradually add the dry ingredient mixture into the wet ingredient mixture, mixing on low speed until just combined. Be careful not to overmix the dough.

Using a small cookie scoop (about 1.5 tablespoons) or rolling the dough by hand, form the dough into uniform balls. Place the cookie dough balls onto the prepared baking sheets, spacing them about 2 inches apart.

Bake the cookies for 9 to 11 minutes, or until the edges are lightly golden brown and the centers are still slightly soft. Remove the baking sheets from the oven and immediately place them on a cooling rack.

While the cookies are still very hot, take the 1/4 cup of extra chilled peanut butter and roll it into very small pea-sized balls (these will be the center pads of the paw). Gently press one small peanut butter ball into the center of each warm cookie. The warmth of the cookie will slightly soften the peanut butter and adhere it to the cookie.

For the 'toes,' take three mini chocolate chips and arrange them in an arc directly above the central peanut butter pad on each cookie. Press them gently into the cookie so they stick. Repeat this process for all baked cookies.

Allow the cookies to cool completely on the baking sheet for 10 minutes before transferring them carefully to a wire rack to finish cooling. This ensures the cookies and the paw prints are fully set. Store cooled cookies in an airtight container at room temperature.