Season both sides of fish fillets with salt and black pepper. Heat oil in a large skillet over medium-high heat. Add halibut and cook 2 minutes per side, until golden brown.
In a medium bowl, combine red peppers, olives, vermouth, garlic, and oregano. Add mixture to pan and bring to a simmer. Cook 2 minutes, until fish is fork-tender. Remove from heat, transfer to a serving platter and top with basil.