Heat 1/2 cup of the olive oil in a large skillet. Add the peppers, onion, garlic and thyme and cook over moderate heat until crisp-tender, about 5 minutes. Add the water and cook over moderately low heat until the vegetables are very soft and the liquid has evaporated, about 25 minutes. Season with salt and 1/2 teaspoon of piment d'Espelette, then transfer to a bowl to cool.
Rub the tuna with the remaining 2 tablespoons of olive oil and season generously with salt and 1/2 teaspoon of piment d'Espelette. Heat a large, heavy skillet. Add the tuna and cook over high heat, turning once, until browned outside and medium rare within, about 4 minutes. Transfer the tuna to a cutting board and slice 1/2 inch thick.
Add the frisée, parsley and vinegar to the peppers, season with salt and piment d'Espelette and toss. Mound the salad on plates and top with the tuna. Sprinkle with salt and piment d'Espelette and serve.