In a small bowl, combine the ricotta cheese, powdered sugar, and vanilla extract. Stir in the semi-sweet chocolate chips and set the ricotta mixture aside.
In a shallow bowl or pie plate, whisk the two large eggs and the 1/4 cup heavy cream (or milk) together until blended.
Lay out the four slices of French bread. Spread the ricotta mixture evenly over two slices (using all of the mixture). Top each filled slice with one of the remaining bread slices to make two sandwiches and gently press them together.
Carefully dip both sides of each sandwich into the egg mixture, allowing excess to drip back into the bowl.
Heat a large skillet over medium heat and melt the 2 tablespoons of butter in the pan.
Add the dipped sandwiches to the skillet and cook until golden brown, about 4 minutes per side.
Transfer the sandwiches to a cutting board, cut each in half on the diagonal, dust with powdered sugar, and serve immediately.