Heat oven to 350°F.  

In a small saucepan, brown the butter by melting it over medium heat, swirling the pan periodically to make sure the butter is cooking evenly.  The butter will start to foam, then turn from a pale yellow to a toasty brown with a nutty aroma.  Let cool for 10 minutes (you can speed up the process by setting the pan in a bowl of ice water, being careful not to let any water get into the pan).

Once the butter is no longer hot enough to cook the egg yolk, add the brown sugar, granulated sugar, egg yolk, water and vanilla to the pan and beat with a handheld mixer until creamy, about 2 minutes.

Add the flour, baking soda, and salt and mix just until combined.  Stir in the chocolate chunks, then spread into one 6 ¼" mini cast iron skillet or two 8-ounce ramekins.

Bake for 17-19 minutes if using the cast iron skillet (approximately 14-16 minutes if using ramekins) until the edges are puffy and slightly crispy while the center is still gooey and slightly underbaked.  

Remove from oven and serve warm, with a big scoop of vanilla ice cream, chocolate sauce or hot fudge, and two spoons!