Create a double-boiler by filling a small saucepan halfway with water and placing over medium-high heat on the stovetop.
Place a large glass bowl over the top of the saucepan, then add the chocolate and butter together in the bowl, stirring occasionally until melted and smooth.
While the chocolate and butter are melting, butter an 8×8 pan, and preheat the oven to 350 degrees.
Once chocolate and butter are melted and smooth, remove the bowl from the double-boiler.
Add sugar and vanilla to the chocolate and mix well.
Add sourdough starter and eggs and mix well with a whisk until the batter is smooth.
Pour batter into your greased pan and bake in the oven, at 350 degrees, for 10 minutes.
Remove brownies from oven, top with chocolate chips, then place back into the oven and continue baking for about 15-20 minutes, or until baked through and a knife, when inserted into the center, comes out clean.
Remove brownies from the oven and let rest on a cooling rack for 10 minutes.