In a large saucepan, bring water and 1/2 teaspoon salt to a boil. Slowly add polenta in a thin stream, whisking; reduce heat to medium and cook, whisking constantly, for 2 minutes. Reduce heat to low and cook, stirring often with a wooden spoon, until thickened and tender, about 40 minutes.

Meanwhile, in a large saucepan heat 3 tablespoons oil over medium heat until warm and fragrant, about 3 minutes. Add mussels. Cook, covered, until mussels just open wide, checking frequently after 3 minutes and transferring open mussels to a bowl using a slotted spoon; reserve the pot with any liquid. Discard any mussels that remain unopened after 8 minutes. When cool enough to handle, detach meat and discard all but 12 half-shells.

Strain mussel cooking liquid through a fine-mesh sieve and return to pot. Add remaining 1/2 cup oil, wine, garlic and peppercorns to pot. Bring to a simmer and cook, uncovered, until reduced by half, 8 to 10 minutes. Remove from heat; stir in parsley.

Place three 1/4 cup scoops of polenta on a plate, top each scoop with a mussel shell. Fill each shell with 2 to 3 mussels, then spoon sauce over the top. Repeat to make 4 plates. Serve warm.