- Preheat the oven to 190°C. Use 1 tablespoon of the butter to grease an approximately 22 x 33 cm pan.
- Melt the chocolate and butter together in a heavy-bottomed saucepan, over low heat. Stir occasionally and heat until the chocolate and butter are completely melted together. Remove from the heat, and set aside to cool to room temperature.
- In a large bowl, use an electric mixer to beat the eggs with the sugar, coffee grounds, vanilla, and salt at high speed for 5 minutes. Then on a low speed, add the cooled chocolate mixture and beat only until mixed. Now add the flour and again beat only until mixed.
- In a small bowl, combine the hot coffee with the Kahlúa, and then pour the mixture into the batter. Mix to blend.
- Pour the batter into the prepared pan and place it in the oven. Bake just until the edges look solid and there is little to no movement in the centre, when you gently jiggle the pan, about 35 minutes.
- Let the brownies cool at least to room temperature before cutting and/or serving.