In a medium saucepan, simmer the strawberries and sugar over medium heat. Cook, stirring occasionally, until softened and syrupy, about 20 minutes. Let cool.
Transfer the ice cream to a large bowl; fold in 1/2 cup strawberry sauce (reserve the remaining sauce for another use). Cover and freeze until firm, about 1 hour.
Place the cookies flat side down on a parchment-paper-lined baking sheet. Top each cookie with 1 small scoop of ice cream. Freeze until firm, about 30 minutes.
In a double boiler, melt three-quarters of the chocolate. Remove from the heat and stir in the remaining chocolate until melted. Dunk each bonbon into the chocolate to coat; return to the prepared baking sheet. Immediately sprinkle with the pistachios. Freeze until firm, about 30 minutes.