If your salmon fillets are skin on, carefully run a knife between the skin and salmon flesh and remove the skin.
Once your salmon is skinless, cut it into 4-5 serving size pieces.
Sprinkle the pieces with kosher salt and black pepper.
Put the flour in a bowl and dredge the salmon in the flour until evenly coated.
Heat the olive oil in a large skillet on medium-high until shimmering.
Add the salmon and sear for 3-4 minutes per side, or until it reaches 125F in temperature. Remove to a plate and tent with foil.
Add the butter to the skillet and swirl until it melts. Then, add the garlic and shallots and stir for 30 seconds.
Add the white wine. Bring to a boil and reduce for 1 minute.
Stir together the stock and cornstarch to make a slurry. Pour the slurry into the skillet and bring to a boil while whisking.
Add the lemon juice and let the sauce boil and thicken for 2-3 minutes, whisking frequently.
Taste the sauce and add kosher salt and black pepper as needed. Then stir in the capers and parsley.
Return the salmon to the skillet and spoon the sauce over. Scatter lemon slices around the skillet. Serve over pasta, rice, mashed potatoes, or any other base of your choice.