Remove the mussels from the shells, reserving the liquid in the bowl. Set aside to chill in the refrigerator. Discard the shells. Strain the cooking liquid through a chinois and set aside to chill in the refrigerator.
To serve, divide mussels between serving bowls and arrange in mounds. Carefully divide soup between the bowls around of the mussels. Top mussels with red pepper and basil.