Cut off the tops of the strawberries and slice the berries. Reserve 2 large whole berries for garnish.
In a blender, place 2 cups of strawberries and 2 tablespoons confectioners sugar; blend to puree and set aside.
In a medium bowl, combine mascarpone cheese, 1/4 cup cream, 1/4 cup sugar, and liqueur; beat with an electric mixer on medium-high speed for 1 to 1 1/2 minutes until thickened.
Place 6 ladyfingers on a serving plate and brush each with approximately 1 teaspoon cold espresso coffee. Spread or pipe out 1/2 of the cheese mixture over the ladyfingers, and layer with half of the sliced strawberries.
Repeat with the next 6 ladyfingers, espresso, remaining cheese mixture, and sliced strawberries; top with remaining 6 ladyfingers.
In a small mixing bowl, combine 1/4 cup heavy cream with 2 tablespoons sugar; beat with an electric mixer on medium-high speed until just whipped, approximately 1 minute. Spread cream evenly over top layer of ladyfingers.
Dust cocoa over whipped cream, and garnish with 2 reserved strawberries. Pour strawberry puree onto two serving plates. Cut tiramisu in half, and place onto puree.