Preheat oven to 400 degrees F.
Tightly wrap sweet potatoes in foil and place on a baking sheet. Roast until very tender, about 1 1/4 hours. Carefully unwrap and set aside to cool.
Reduce oven temperature to 350 degrees .
Process gingersnaps in a food processor until finely ground. Transfer to a bowl, add oil and stir until well combined. Using a spoon, spread and pat the crumbs into the bottom and up the sides of a 9-inch pie pan. Bake until just barely beginning to darken, about 10 minutes.
Clean and dry the food processor workbowl. Peel the sweet potatoes and transfer to the food processor. Puree until smooth. Measure out 1 1/2 cups (if you have extra puree, reserve it for another use). Return the 1 1/2 cups puree to the food processor. Add brown sugar, 1/2 cup yogurt, eggs, egg yolk, cinnamon and nutmeg; pulse just until combined. Spread the sweet potato filling in the warm crust.
Clean and dry the workbowl again. Add the remaining 1/4 cup yogurt, cream cheese, confectioners’ sugar and ginger; puree until smooth, stopping to scrape down the sides once or twice. Dollop tablespoonfuls of the cream cheese mixture onto the filling, spacing them evenly. Draw the tip of a wooden skewer or a thin knife through the cream cheese mixture and sweet potato filling repeatedly to create a swirled design.
Bake the pie until firm to the touch and starting to puff around the edges, 45 to 50 minutes. Let cool completely on a wire rack, at least 2 hours.