Combine flour, salt, white pepper and garlic powder in a small bowl. Dust fish with flour mixture.
Heat 2 tablespoons of the butter and the olive oil in a large skillet over medium heat. Add fish and brown on one side, about 3 – 4 minutes. Flip fish over and cook for 2 more minutes. Remove fish and keep warm.
Add wine and lemon juice and stir to loosen bits stuck to pan. Reduce liquid to just a few tablespoons. Stir in basil and remaining chilled butter, stirring until butter is melted. Remove from heat.
For each serving, arrange 1 slice of tomato on a plate. Top with 1 piece of fish and then avocado slices. Place tomato over avocado, then fish and then 2 mores slices avocado. Drizzle butter sauce over and serve.