Place the white beans in a medium pot with water covering the beans by 2 inches. Bring water to a boil, then lower heat to a simmer for about 45 minutes.
Meanwhile, season the crappie fillets liberally with salt and pepper.
Drizzle olive oil into a heated sauté pan. When oil is shimmering, place crappie in pan and cook for 3 minutes. Lower heat to medium. Turn over fillet and cook for another 2-3 minutes. Remove from heat and repeat with remaining fillets.
Add basil, parsley, and lemon juice to the beans and return to a boil, then lower to a simmer.
Season the beans with salt and divide among 6 shallow bowls. Top each bowl of beans with a crappie fillet. Garnish with remaining chopped basil and parsley, then drizzle on some olive oil.