Pat the sole fillets dry with paper towels and season both sides with salt and pepper.
Lightly dredge each fillet in flour, shaking off excess.
Heat butter and olive oil in a nonstick skillet over medium-high heat until shimmering.
Add the fillets and cook 3 minutes on one side until golden brown and edges begin to set.
Flip gently and cook another 3 minutes, until fillets are opaque and flake easily.
Remove the fillets from the pan and keep warm on a plate.
Add garlic to the same skillet and sauté for 30 seconds until fragrant, not browned.
Deglaze the pan with lemon juice, scraping up any browned bits.
Stir in capers and parsley, heat briefly, and spoon the sauce over the fillets.
Serve immediately with lemon wedges on the side.
