Preheat oven to 350F. Add eggs and sugar to a large mixing bowl and mix with an electric mixer. Mix until light and fluffy - about 3 minutes.
Chop chocolate bar into chunks and melt with butter in the microwave or over a double boiler. Only warm until the butter is just melted. Mix until evenly combined and pour chocolate and butter mixture into the eggs and sugar along with the vanilla extract. Mix again with the electric mixer.
Add cocoa powder, flour, and salt to the bowl and fold in with a spatula. Mix until the dry ingredients are just folded in.
Grease a mini muffin pan (or use muffin lines) and add 2 tbsp of batter to each of 24 muffin slots. Place in the oven and bake at 350F for 15-17 minutes. Remove from the oven and allow to cool COMPLETELY before removing from the muffin pan. Removing from the pan prior to cooling may make them crumble.
Notes
Do not overbake. Brownie bites cook fast in a mini muffin pan. Pull them out when the edges look set and the center still looks a little soft. They will firm up as they cool.Grease the pan really well. Use cooking spray or butter in every cup and get into the edges. Brownie batter is sticky and will stick if the pan is not well coated.Let them cool in the pan. Give the brownie bites at least 10 minutes to cool in the pan before trying to remove them. They are very soft when hot and will fall apart if you rush it.Use good quality cocoa powder. The chocolate flavor in this recipe comes mostly from the cocoa powder so using a good quality one makes a big difference.