Season both sides of salmon fillets evenly with salt and lemon pepper (if your salmon has the skin on, just season the skinless side). Place 1/4 cup of flour in a shallow dish, and dip the salmon (skinless side(s) only) in to coat, and shake off any excess, and set aside.
Melt 1 tablespoon of butter with 1 tablespoon of olive oil in a large non-stick skillet over medium-high heat. Add the salmon fillets (skin side down if it has the skin on), and cook for about 4 minutes to get a nice sear, before gently flipping with tongs. Cook for an additional 4 minutes, or until cooked through. If you had skin-on salmon, use the tongs to gently pull the skin off during this phase, then flip back over for just a minute to get a good sear on that side as well. Remove salmon to a plate and keep warm while you prepare the sauce.
Using the same skillet, add the remaining tablespoon of butter and melt over medium heat. Add the garlic and sauté for about a minute, until fragrant. Pour in the wine (or chicken broth if you are using that instead) and bring to a boil, scraping up any browned bits from the bottom. Cook for 2-3 minutes, or until liquid almost evaporates, stirring occasionally. Add ¾ cup broth and the lemon juice, bring to a boil and cook for an additional 3 minutes.
Meanwhile, combine the remaining 1/4 cup of broth and 3 tsp of flour in a small bowl and whisk to combine. Add this mixture to the skillet and stir until well-combined and slightly thickened, about a minute.
Remove from heat and stir in capers. Return the salmon fillets to the pan, gently turning each fillet to evenly coat in the sauce. Garnish with chopped parsley and lemon pepper, if desired. Serve immediately with extra lemon wedges!