Cut 10 ladyfingers in half, crosswise. Separate the cut pieces and place them cut side down, around the sides of an 8-inch springform pan. Split remaining ladyfingers and arrange cut side down on bottom of pan; set aside.
Pour 1/2 cup milk into a food processor or blender. Add cream cheese cubes and process until smooth. Use a rubber spatula to scrape sides of blender container. Add remaining 1 cup of milk and process until smooth.
Dissolve instant espresso in hot water. Add dissolved espresso, rum extract and pudding mix to cheese mixture. Process until smooth, scraping sides once or twice. Pour into a large bowl; stir in (thawed) whipped topping until well blended. Spoon onto crust; smooth top. Cover with plastic wrap, making sure wrap does not touch pudding. Chill until firm, 8 hours or overnight.
When ready to serve, use a sharp knife to loosen dessert from sides of pan. Remove sides of pan and place pudding cake on serving plate. Sprinkle with cocoa and garnish each serving with a whole strawberry.