I don't know if I can replace the brown sugar with white sugar because the recipe already calls for white sugar too.
Many recipes require both brown and white sugar. It is possible to substitute the brown sugar for the white sugar 1:1 but several things will change in your final result.
- Taste - Brown sugar is essentially white sugar with molasses. The molasses adds a malty thick complex sweetness. With just white sugar your cookie will have a less complex flavor.
Note: To combat #1, you can add a little bit of: honey, dark corn syrup, maple syrup, brown rice syrup or barley malt syrup to make up for the flavor loss.
- Texture - The white sugar will melt at a lower temperature meaning it will not be able to hold the shape of the cookie before the gluten sets. The sugar will melt and cause the dough to spread out. When using brown sugar, the dough will be able to set before the brown sugar melts. So when baking cookies, using all white sugar will result in a flat/thin crunchy cookie while using more brown sugar will result in a thicker, softer cookie.
Note: To mitigate #2 you can chill your dough before you bake the cookies to help prevent your dough from spreading too thin during the baking process.
If however you do have molasses, you can easily create your own brown sugar by mixing 1 cup white sugar with 1 tbsp molasses.