Have ready four 4-ounce parfait glasses. You can also use cocktail glasses, custard cups or ramekins, preferably glass, of about the same capacity.
Mash the ricotta, milk and 2 tablespoons of confectioner's sugar together in a small bowl with a rubber spatula until the mixture is smooth. Mix the coffee, rum, and remaining tablespoon confectioner's sugar together in another small bowl.
For each serving, put the equivalent of one cookie, or about 2 tablespoons of crumbs, in the bottom of a parfait glass. Sprinkle with a scant 2 teaspoons of the coffee mixture. Top with a scant 2 tablespoons of the ricotta mixture. Repeat with the cookie crumbs, coffee mixture, and ricotta mixture. Cover each with plastic wrap and refrigerate until chilled, which takes at least one hour and up to one day.
Just before serving, top each tiramisù with an equal amount of berries. Using the large holes on a box grater, grate the chocolate onto a sheet of waxed paper. Lift up the waxed paper and use it to help sprinkle the chocolate over the berries. Note that if you touch the grated chocolate, it will melt. Serve chilled.