Leave the butter to soften at room temperature. Add chopped parsley and thyme, season with salt and pepper, and mash it together with a fork until it forms a coherent wodge of herb butter.
Clean the baby carrots leaving a little of the green stalk for presentation. Finely chop the radish and chili. Season with salt and drizzle with the juice of half a lime.
Get the barbecue going on a medium heat and put on the carrots, drizzled with olive oil. Let them cook for around 15 minutes until they begin to soften.
Now get the barbecue going full power. Pat the fillets dry and season with salt and pepper. Put the bream on the barbecue skin side down and cook for around 5 minutes. Then close the grill for 2 minutes, leaving a little room above the fish so it cooks from above but doesn't burn or dry out.
Toss the carrots around in a bowl with a good scoop of the herb butter until they are thoroughly coated. Now plate these up with a drizzle of the butter from the mixing bowl. Place the fish skin side up on top of the carrots and, once again, generously add the herb butter along its length. Garnish with the radish salsa.