To make Lemony brown butter:
Melt butter in a medium saucepan, preferably not non-stick, set over medium. When butter becomes foamy, stir often until it smells nutty and turns dark brown, about 4 min. Immediately remove from heat and pour into a small bowl, then stir in 2 tbsp fresh lemon juice and 1 tsp lemon zest. Use right away or refrigerate up to a week. To melt Brown Butter, microwave on high for 15 to 30 sec.
To make Lemony fish fillet:
Heat a large non-stick frying pan over medium-high. Add 1 tsp olive oil, then 4 sole fillets. Cook until a knife tip inserted into thickest part of fish and held for 10 sec comes out warm, about 2 min per side. Transfer to 4 plates. Add 2 tbsp Lemon brown butter, 1 minced garlic clove, 1 tbsp chopped capers and 2 tbsp chopped parsley to pan. Stir until sauce is warm. Spoon over fish.