Preheat your oven to 350°F (175°C).
In a medium saucepan, combine 2 tablespoons of butter and 2 tablespoons of water over low heat. Once melted, add 1 1/3 cups of semi-sweet chocolate chips and stir until smooth. Remove from heat and cool slightly.
In a large mixing bowl, whisk together 2 large eggs and 1/2 cup of granulated white sugar until well combined. Add the chocolate mixture and 1 teaspoon of vanilla extract, mixing until incorporated.
In another bowl, whisk together 2/3 cup of all-purpose flour, 1/4 teaspoon of baking soda, and 1/4 teaspoon of salt. Gradually fold the dry ingredients into the wet mixture until just combined.
Pour the brownie batter into the prepared pie dish, spreading evenly. Bake for 25 to 30 minutes, or until a toothpick comes out with a few moist crumbs. Allow to cool.
In a small saucepan, combine 1 cup of semi-sweet chocolate chips, 1/2 cup of evaporated milk, 1/4 cup of granulated white sugar, and 1 tablespoon of butter. Heat over low, stirring until smooth. Remove from heat and cool slightly.
Once the brownie pie has cooled, pour the chocolate topping over it, spreading evenly. Let it set, then slice and top with vanilla ice cream.
