Using a sharp serrated bread knife, cut the baguette into slices approximately 1 inch thick. Place the pieces in a single layer on a large tray so they are ready for grilling.
Spread the 2 tablespoons of butter evenly over one side of the baguette slices.
Warm a grill or grill pan over medium heat. Arrange the bread with the buttered surfaces facing downward.
Grill for 1–2 minutes on each side, or until the bread becomes crisp and distinct grill marks develop. Transfer the toasted slices from the heat and allow them to cool slightly.
Place the pomegranate arils in a small bowl and add the juice from half a lemon along with the finely chopped fresh mint.
Gently toss the ingredients until they are evenly combined.
Season the mixture with salt and black pepper according to taste, then stir once more. Taste the topping and adjust the seasoning as necessary for the desired balance of freshness and acidity.
After the grilled baguette slices have cooled slightly, spread a generous coating of softened cream cheese over the top of each piece.
Spoon the prepared pomegranate and mint mixture over the cream cheese layer on each grilled baguette slice, distributing the topping evenly among the pieces.
Serve the pomegranate bruschetta immediately while the bread remains crisp and the topping is fresh.