Season flour with salt and pepper, to taste. Mix eggs and 2 tablespoons clarified butter to make egg wash. Season with salt and pepper. Coat each fillet in flour, then egg wash, then breadcrumbs. Shake to remove excess.
Heat clarified butter in large baking dish over medium-high heat and fry fish, turning once after 2 minutes. Add bananas alongside fish and cook, turning once. Cook fish for 4 minutes on second side. Remove from pan and place on heatproof platter, garnish with bananas and tomato and lemon slices. Season with salt and pepper. Preheat broiler.
Pour lemon juice in double boiler and stir in egg yolks. Season with salt and pepper. Add 2 ounces fresh butter to egg/lemon mixture and whisk until smooth, careful not to overcook. Stir in remaining butter to finish sauce and add chives.
Meanwhile, broil garnished fish for 4 minutes until brown. Serve immediately, napped with sauce.
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