Place the cream cheese, mashed sweet potatoes, 1/4 cup sour cream, 1/4 cup granulated sugar, 1/2 cup packed light brown sugar, 2 teaspoons vanilla extract, 1 teaspoon ground cinnamon, 3/4 teaspoon kosher salt, 1/4 teaspoon ground nutmeg, and 1/8 teaspoon ground ginger in the food processor. Process until combined, about 1 minute. Add the eggs one at a time, processing to combine after each, until all the eggs incorporated, about 40 seconds total.