Preheat the oven to 325 degrees F. Grease an 8-inch square Pyrex dish and line with a strip of parchment so that the brownies can be removed from the pan.
In a large saucepan, gently melt the butter. Add the water and both sugars and bring to a boil. Remove from heat and stir in chopped chocolate and chocolate chips until melted and smooth. Chocolate will begin to thicken as you stir.
Whisk the cold eggs in a second bowl until very light and frothy, then whisk or stir them into the chocolate mixture. Whisk in the vanilla.
Combine the flour, baking soda and salt; stir into the chocolate mixture. Add the remaining chocolate chips (make sure that the batter is not so hot that it melts them) and spread batter evenly into the prepared pan.
Bake the brownies at 325°F for 25 to 32 minutes (mine usually take 32), or until the center no longer looks wet and the brownies appear set around the edges. Because glass pans retain heat, the brownies will continue firming up as they cool, so it’s better to err slightly on the underbaked side than overbake them. If you like using a thermometer, the center will usually be somewhere around 180°F to 190°F when done, with the fudgiest texture closer to the lower end of that range.
Let cool completely at room temperature, then chill slightly before serving. Lift from pan and slice.