To prepare espresso drizzle, combine first 3 ingredients in a small saucepan over medium-high heat; bring to a boil. Cook 1 minute, stirring occasionally. Remove from heat; stir in 2 tablespoons liqueur. Cool completely.
To prepare filling, combine cheeses in a large bowl, and beat with a mixer at medium speed until smooth. Add 1/3 cup granulated sugar, brown sugar, and 2 tablespoons liqueur; beat at medium speed until well blended.
Split ladyfingers in half lengthwise. Arrange 24 ladyfinger halves, cut sides up, in the bottom of an 8-inch square baking dish. Drizzle half of espresso drizzle over ladyfinger halves. Spread half of filling over ladyfinger halves, and repeat procedure with remaining ladyfinger halves, espresso drizzle, and filling. Combine 1 1/2 teaspoons cocoa and chocolate; sprinkle evenly over top of filling. Cover and chill for 2 hours.
Note: Place toothpicks in the center and in each corner of the dish to prevent the plastic wrap from sticking to the tiramisu as it chills.