In a small saucepan set over medium heat, brown the butter. Stir the butter occasionally until it turns amber in color and develops little brown specks.
Transfer the brown butter to a small heat-safe bowl. You should be left with at least 90g of brown butter (but not more than 95g). If you have a little less than 90g, just add in some water until you reach it.
Place the brown butter in the freezer for 5 minutes to cool down.
In the meantime, chop your white chocolate and pour the granulated sugar into a medium-sized mixing bowl
Zest the limes into the bowl of sugar, then use your hands to rub together the zest and sugar until sugar is fully coated and kind of resembles wet sand.
Add in the brown sugar and the brown butter once it has slightly cooled, then mix together until combined.
Whisk in the egg and vanilla until well combined.
Add in the flour, baking soda and salt. Use a rubber spatula to fold the mixture together just until a few flour streaks remain.
Add in the white chocolate and fold just until no flour streaks remain.
Cover the dough and chill it for at least 15 minutes. Annoying, I know - but so worth it and necessary to ensuring your dough doesn't spread too much!
Preheat the oven to 350°F / 175°C. Line a cookie sheet with parchment paper or a silicone baking mat.
Scoop out heaping 3 tbsp. scoops of dough (or use a 1/4 measuring cup), setting them on the cookie sheet at least 2" apart to allow room for spreading.
Top each cookie with additional white chocolate and a little bit more lime zest if desired, and bake for 12-14 minutes, or until the edges of the cookies are golden brown.
Immediately after taking the cookies out of the oven, you can take a bowl that is slightly larger than the cookies and swirl it around over the cookies to make them a little more uniform and circular.
Serve and enjoy!