Preheat the oven to 190C/375F degrees.
Line a square baking tin (or you could use a circular one...no rule on shapes!) with greaseproof paper.
Mix the brownie ingredients first.
Mix the dry ingredients in a bowl.
Melt the butter and chocolate in a Bain Marie (bowl over simmering water).
Remove from the heat and cool for 5 minutes.
With a whisk, (electric is better) add the eggs, one at a time. Add the vanilla essence.
Add the dry ingredients and mix thoroughly.
Spread the mixture in the tin evenly.
In a bowl, beat the cream cheese mixture with an electric whisk until smooth.
Add the vanilla essence and erythritol and beat well.
Add the eggs, one at a time.
Put half the mixture in another bowl and add the melted chocolate. Mix well.
Place the cheesecake mixture over the brownie base in an uneven distribution of the vanilla and chocolate cheesecake mixture.
Swirl the chocolate and vanilla mixture lightly together.
Bake in the oven for 30 minutes until slightly firm. Don't worry if the centre is slightly jiggly as the cheesecake part needs to set later.
Cool and then chill in the refrigerator for at least 2 hours.