For the oven-roasted tomatoes: Preheat the oven to 350 degrees F. Place the tomatoes in an oven-safe pan or small baking dish. Top the tomato halves with the olive oil, thyme, garlic, onion and some salt and pepper. Cover the pan with foil and cook until nice and soft, 25 to 35 minutes.
Remove from the oven and let cool. When cool enough to handle, peel off the tomato skins and break up the tomatoes with your hands. Refrigerate until ready to use, up to one week.
For the eel: Heat a large skillet over medium heat with 2 tablespoons of the olive oil. Add the potatoes to the pan and cook, tossing occasionally, until golden brown and tender, about 10 minutes. Season with salt and pepper.
While the potatoes are cooking, place a second large skillet over medium-high heat with the remaining 2 tablespoons olive oil. Sprinkle the eel fillets with salt and pepper. Sear the fillets, turning once, until golden brown, about 90 seconds per side. Add 2 cups of the roasted tomatoes, the olives and capers to the skillet and continue cooking until the sauce has thickened and the eel is cooked through, 5 to 7 minutes. Adjust the seasoning with salt and pepper. Reserve the remaining roasted tomatoes for another use.
To serve, divide the potatoes among the plates and top with the eel fillets. Spoon the tomato sauce over each plate and garnish with the herbs.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.