Pat the fish dry with a paper towel. In a shallow dish, mix together the flour (1/4 cup), salt (1 teaspoon), and black pepper (1/2 teaspoon).
In a large skillet, preferably stainless steel or nonstick, melt 1 tablespoon of the butter over medium high heat and add the olive oil (1 tablespoon).
Cook the fish in the skillet for 3-4 minutes on each side, until golden brown and fully cooked. Try not to move the fish too much, especially if you are using a pan that isn’t nonstick, otherwise the fish may be more likely to stick to the bottom and not get browned as nicely.
Remove fish from the skillet to a plate.Turn down the heat to low. Add the white wine (1/4 cup) to the skillet to deglaze, stirring up any browned bits. Continue heating until almost all the wine has evaporated.
Add one more tablespoon of butter to the skillet. Once it’s melted, add the minced garlic (2 cloves) and fresh herbs (1 tablespoon each of oregano, thyme, and parsley) to the skillet and sauté until fragrant, about 30 seconds.
Add the chicken broth (1/2 cup) and bring to a simmer. Turn off heat and stir in remaining 1 tablespoon butter and lemon juice (about 2 tablespoons). Taste and adjust seasoning if necessary. Serve sauce on top of fish.