Put oven rack in middle position and preheat oven to 350°F.
Pulse sugar and ginger in a food processor until ginger is finely chopped, then add cream cheese and pulse until smooth.
Add eggs, milk, flour, nutmeg, and salt and pulse until just combined.
Reserve 2/3 cup cream cheese mixture in a glass measure.
Whisk together remaining 1 1/3 cups cream cheese mixture and pumpkin in a large bowl until combined.
Pour pumpkin mixture into gingersnap crumb crust. Stir reserved cream cheese mixture (in glass measure) and drizzle decoratively over top of pumpkin mixture, then, if desired, swirl with back of a spoon. Put pie on a baking sheet and bake until center is just set, 35 to 45 minutes.
Transfer to a rack and cool to room temperature, about 2 hours, then chill, loosely covered with foil, at least 4 hours. If necessary, very gently blot any moisture from surface with paper towels before serving.
