Preheat your oven to 375 degrees Fahrenheit.
In a stand mixer, combine the softened butter with the dark brown sugar and granulated sugar until well mixed.
Add the eggs and continue mixing until the eggs are completely incorporated.
Now pour the vanilla extract into the cookie dough and mixer for 30 seconds to combine.
Add the chunky peanut butter to the bowl and mix for 2 minutes, or until the peanut butter is completely mixed into the dough.
Now add the salt, baking soda, and flour and mix slowly for 2-3 minutes. The dough should be very sticky.
Scoop the dough onto un-greased baking sheets (2-3 tablespoons per cookie). Lightly press the cookie down to form a small disk (do not use a fork!).
Bake for 8-10 minutes or until the edges start to brown. Remove from the oven and let sit for a minute before moving to a cooling rack. Once the cookies are cool to the touch, move them to the refrigerator or freezer to cool completely.
While the cookies are cooling, separate the white chocolate chips into 3 bowls and add 2 teaspoons of shortening to each bowl. Microwave for 60-90 seconds to melt the chocolate. Add red coloring to one of the bowls and blue to another.
Once the cookies are cooled, place the cookies upside-down into the plain white melted chocolate to coat the top of the cookie. Place back in the refrigerator or freezer so that the chocolate can harden.
To add the red and blue stripes, use a spoon to spread the red and blue chocolate over 1/3 of the cookie. Again, place back in the refrigerator or freezer to harden. Store in the refrigerator until serving.