Preheat oven to 350 degrees Fahrenheit. Line a cookie sheet with parchment paper.
Add light brown sugar, molasses, peanut butter, vanilla, vegetable oil, water, and eggs to a large mixing bowl. Stir ingredients until a creamy mixture forms.
Add white cake mix and salt to the bowl. Stir to combine ingredients. The cookie dough should be thick at this point. Stir in ½ cup peanut butter baking chips, if desired.
Use a small ice cream scoop to remove about 1-½ to 2 Tbsp of peanut butter cookie dough from the bowl. Shape into a ball, and then flatten the ball slightly.
Gently press a small amount of the remaining peanut butter baking chips into each cookie dough round. Divide the peanut butter chips evenly among the cookies.
Place the peanut butter cookie rounds on a cookie sheet to bake. Leave 2 inches between each cookie on all sides. It may be necessary to bake cookies in batches, depending on the size of the cookie sheet.
Bake the peanut butter cookies on the center oven rack for 8 to 10 minutes, or until a toothpick inserted into the center of the cookies comes out clean.
After removing the cookie sheet from the oven, let the cookies rest on the cookie sheet for 5 minutes. Then use a spatula to move the cookies to a cooling rack to cool before serving.