In a large mixing bowl, beat cream cheese until smooth.
Beat in sugar and vanilla.
Beat in eggs, one at a time.
Line muffin pans with regular-sized muffin cups with paper liners.
Place one whole Oreo cookie at the bottom of each cupcake liner.
Fill the muffin cups 1/2 full with cheesecake batter.
Add pumpkin puree, cinnamon, pumpkin pie spice, ginger, and clove to remaining cheesecake batter.
Top the regular cheesecake batter with pumpkin cheesecake batter, til the muffin cups are 3/4 full.
Bake at 350°F for 18-22 minutes, or until cheesecakes are set.
Place the pans on a wire rack to cool completely.
Remove the cheesecakes from the muffins pans, and remove the paper cupcake liners.
Drizzle with melted white chocolate (optional). Store in refrigerator.