Combine first 5 ingredients in a medium saucepan over high heat, whisking until smooth. Bring to a boil; reduce heat, and simmer until reduced to 3/4 cup (about 25 minutes).
Remove from heat. Stir in lime juice, mint, and basil; let stand 5 minutes. Strain into a measuring cup; discard solids. Keep sauce warm.
Heat a large nonstick skillet over medium-high heat.
Add oil; swirl to coat.
Sprinkle fish evenly with pepper and salt.
Add fish to pan; cook 4 minutes on each side or until desired degree of doneness.