In a bowl, mix the cream cheese and vanilla extract until smooth. Mix in the guava paste, then transfer the mixture to a piping bag.
With a small serrated knife, create a pocket inside each brioche slice by inserting the knife in the middle of the crust on the bottom side, making sure not to cut through to the other end of the slice. Pipe about 4 tablespoons of the filling into each pocket.
Heat a griddle over medium heat.
In a shallow dish, whisk together the cream, granulated sugar, cinnamon, salt and eggs. Dip a piece or 2 of the stuffed brioche in the custard mixture and allow to soak for 30 seconds on each side.
Add 1 tablespoon of butter to the griddle per brioche slice. When melted, gently transfer the soaked slices from the custard to the griddle. Cook until the bread is golden, the custard is cooked and the filling is warm, about 2 minutes each side. Soak and cook the remaining stuffed slices, adding the remaining butter to the griddle.