Slice the apricots in half, carefully remove the pits, and set aside. Combine the ricotta cheese with the ginger and 2 teaspoons of the honey in a mixing bowl.
Place the apricot halves on a serving platter and top each with a spoonful of the honey-ginger-ricotta mixture. Sprinkle the pistachios on top, and drizzle with the remaining teaspoon honey. Serve immediately.