Start by combining the baby arugula, diced avocado, tomatoes in a large salad bowl. Toss with balsamic vinegar and salt and pepper to taste. Set aside.
Place a large cast iron skillet over medium-high heat. Once hot, add a little olive oil. You need less than a inch of the oil. Just enough coat the bottom good.
Add the fish to the hot oil and cook for 4-5 minutes, or until golden brown and it releases easily from the bottom of the skillet. Turn the heat down to medium and flip each filet. Cook for another 4-5 minutes, or until the fish is cooked through and the fish flakes easily with a fork.
Transfer to a wire rack or a platter lined with paper towels and set aside. Deglaze your skillet by adding the white wine and gently scraping the bottom with a plastic spatula to release the browned bits.
Add the butter, lemon juice, zest, and thyme sprigs. Generously season with salt and black pepper, to taste, and stir to combine. Cook for 1-2 minutes, or until heated through. Remove from heat and discard the thyme stems in the sauce.
Add the fish back to the skillet just long enough to absorb some of the warm butter sauce. Transfer fillets to individual serving plates and spoon some the pan sauce on top.
Top with the avocado, tomato salad and some crumbled Feta cheese, if desired.