1. Place a skillet over medium heat and pour olive oil in it. Spread it all around.
2. Throw chopped shallots in it, and let it to sweat. You must not brown shallots.
3. Remove skillet from heat and add white wine to it. Return it to medium high heat.
4. Pour clam juice in it. When simmer returns insert tilapia to skillet. Turn the heat to slow simmer, keep a watch and poach tilapia for about 8 minutes. Remove and allow it to rest on a plate.
5. For sauce, turn the heat to medium high and reduce the liquid. When the liquid reduces to 2/3rd, add basil paste to it. Whisk.
6. Stir in some butter and diced tomato. Season with salt, pepper and lime juice.
7. Serve tilapia hot with sauce and lemon wedge garnish.