In a medium skillet add the butter over medium heat.
Let the butter melt and then continue to cook, swirling the pan occasionally, until it has browned. The butter will foam a little right before it browns, and you'll want to carefully watch it at this point. Once you see golden brown specks on the bottom, remove the pan from the heat so it doesn't end up as burnt butter.
Let the butter cool for 30 minutes.
After 30 minutes, preheat the oven to 350 degrees F and line 2 baking sheets with parchment paper.
Add the cooled brown butter, granulated sugar, and brown sugar to a large bowl with an electric mixer. Beat until creamy, about 1 minute.
Add the eggs and molasses and beat until combined, scraping down the edges as needed.
Add the baking soda, ginger, cinnamon, and salt, beating until combined and scraping down the edges as needed.
Add the flour and beat until combined.
Place about ½ cup of sugar in a shallow bowl.
Form the dough into ~2 tablespoon sized balls and roll them in the sugar.
Place them on the prepared baking sheets at least 2" apart. Six cookies fit on each of my baking sheets.
Bake in the preheated oven for 8 minutes. Don't overbake!
Cool and enjoy!