Drizzle the olive oil over the salmon fillets and season with some sea salt and white pepper. Set aside.
Fill a high-sided large skillet one-third of the way up with water. Add the wine and lemon halves. Bring to a low simmer, add the salmon and let cook until firm to the touch, 5 to 7 minutes for medium. For well-done salmon, cook for 10 minutes.
Serve garnished with the lemon wedges and parsley.