Put flour in pie plate and season with salt and pepper.
Dredge fish in flour.
Heat skillet over medium-high heat until hot and add 1 T. evoo and 1 T. butter. Add fillets, skin up, and cook until brown on bottom (2-3 min). Add bacon to pan while halibut is cooking and stir to brown.
When bottom is brown, flip fish and put pan in oven until fish is cooked through. About 10 min - more depending on thickness of fillet.
Remove fish to serving plate. Put bacon on paper towels and pat dry. Put skillet back on med-high heat. Add the remaining butter, oil, lemon juice, white wine, capers and parsley and bring to a boil. Boil until reduced and thickened. Season with salt and pepper. Pour over fish, top with bacon, garnish with more parsley (if desired) and serve.