Sprinkle the sole fillets with the thyme and season with salt and pepper. Fold each fillet into thirds and refrigerate.
In a small saucepan, simmer the vinegar until reduced to 1 tablespoon. In a medium saucepan, bring the stock to a simmer. Stir in the tomato paste; cover and keep warm over low heat.
Heat 2 tablespoons of the oil in a large saucepan. Add the onion; cook over low heat, stirring, until softened. Stir in the rice until evenly coated. Add the wine; simmer over moderate heat, stirring, until fully absorbed. Add 1 cup of the hot stock and cook, stirring constantly, until almost absorbed. Add 5 more cups of stock, 1 cup at a time, stirring until absorbed between additions. The risotto is done when it is creamy and the rice is al dente, about 20 minutes total. Cover and keep warm.
In a medium skillet, heat the remaining 1 tablespoon of olive oil until shimmering. Add 2 tablespoons of the butter and the sole, folded side down. Cook over moderate heat, basting often with the butter, until browned on the bottom, about 3 minutes. Reduce the heat to low, turn the fish and baste again. Cover and cook until the fish is white throughout, about 4 minutes longer.
Rewarm the risotto over moderate heat, then stir in the remaining 1/2 cup of stock. Add the olives, sun-dried tomatoes, Parmesan and the remaining 1 tablespoon of butter; season with salt and pepper. Spoon the risotto into shallow bowls; set the fish on top and drizzle the reduced balsamic vinegar around it. Top the fish with the arugula and serve.
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