Preheat the oven to 180°C (350°F) Gas mark 4.
Line an 8-inch square baking tin with parchment paper.
In a medium-sized pan stir the butter and the chocolate over medium-low heat until melted and smooth.
Remove from the heat; Add the sugar, flour, eggs, and vanilla and blend well.
Spoon batter into the prepared tin.
Bake the brownies for 20 minutes (centre should be slightly underbaked).
Allow to cool on a baking rack and then cut into large squares and serve.
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