Add the chopped piloncillo to the hibiscus water and stir until fully dissolved. Let the mixture cool for approximately 15 minutes. Once cooled, strain the warm liquid into a 1-gallon pitcher using a wire mesh strainer, pressing the petals to extract as much liquid as possible before discarding them. Stir in the white sugar until it dissolves, then add enough cold water to fill the pitcher. Serve immediately, or let it stand overnight for the best flavor.