Remove cooled mussels from shells and discard shells. Set mussels aside.
In a 14 to 16-inch saute pan, heat the olive oil and add the garlic. Cook gently 1 to 2 minutes, until softened but not browned. Add the anchovies and chili flakes and toss over heat 1 to 2 minutes. Add the mussels, reduced cooking liquid and vinegar and simmer 1 to 2 minutes. Remove from heat and allow to cool. Place mixture in a large bowl, cover tightly with plastic wrap and refrigerate for several hours or overnight. Add the parsley, toss well and serve.