Preheat the oven to 350 degrees F. Spray an 8 or 9 inch square pan with nonstick spray or line with parchment paper and spray the parchment. (Note: an 8 inch pan will yield thicker brownies like you see in the photos on this post.)
Combine the chocolate and butter in a saucepan over low heat, stirring often until melted and smooth. Remove the pan from heat and let cool slightly.
In a large bowl, use a hand mixer to beat the eggs and sugar together until thick. Mix in the vanilla, and then gradually mix in the chocolate. Then mix in the cocoa powder.
Scrape the batter into the prepared pan and spread it into an even layer. Bake 30 to 35 minutes or until the center is just set. Cool completely before cutting. I like to refrigerate these and cut them when they are well chilled (they cut better).
Notes
If you are making this recipe gluten free, just be sure to use brands of chocolate and vanilla extract that are known to be GF.
Store in a covered container for a day or two or freeze in a covered container and enjoy over the course of a couple of weeks.