Wrap salmon tightly with plastic wrap and freeze for 30 minutes.
Using a sharp knife, slice the salmon against the grain into very thin slices. Place on serving platter and cover with plastic wrap. Refrigerate for 30 minutes or until ready to serve.
Meanwhile, warm olive oil in a small skillet, over medium-high heat. Add the capers and fry for 30-40 seconds. Transfer the capers to a paper towel–lined plate. Pour the oil into a small bowl and let cool for 5 minutes.
Add the lemon juice and parsley to the bowl with the caper oil and whisk until the dressing is emulsified.
Arrange the red onion slices and capers on top of the salmon and drizzle with the dressing. Season lightly with flaky salt and serve with lemon wedges. Enjoy!
