For the rice:
Add the chicken broth to a small saucepan and bring to a simmer.
In a 4 to 5-quart heavy nonstick saucepan over medium-high heat, melt 2 tablespoons of the butter with 2 tablespoons of the olive oil. Add the onion and cook, stirring occasionally, until the onion is soft and translucent, 3 to 4 minutes. Do not allow the onion to brown.
Add the rice and garlic and cook, stirring constantly, until the grains turn white and opaque and smell nutty and the garlic is fragrant, about 2 minutes. Add the white wine, salt and pepper, and stir to combine.
Using a ladle, begin adding the hot broth mixture to the saucepan, 1 ladle at a time, stirring frequently and not adding more liquid until the prior addition is completely absorbed by the rice. The rice should take about 18 to 20 minutes to cook, and you might not need quite all of the liquid. (Or, if you have used all of the broth and the rice is still not cooked through, add a bit of hot water.) The rice should be very smooth and creamy, and the grains should be separate and tender without being mushy.
For the fish:
When the rice has cooked about 15 minutes, season the bronzini fillets on both sides with salt and pepper and heat a large skillet over medium high heat. When hot, add remaining 2 tablespoons olive oil and sear the fillets, skin side down, until golden. Turn to the other side and cook until fish is golden on the presentation side and just cooked through, 1 to 2 minutes, depending on the size of the fillets. Remove from the heat and set aside.
By the time you are finished cooking the fish, the risotto should have reached the proper consistency. Remove the saucepan from the heat and add the arugula, remaining 2 tablespoons of butter, and the grated Parmesan. Stir to combine well and serve immediately, with each guest getting a generous spoonful of risotto in the center of a large shallow rimmed bowl. Top each portion of risotto with a piece of fish, and ladle the Provencal sauce over and around the fish and risotto. Garnish with a pinch of freshly ground black pepper and Parmesan curls, and herbs, if desired.