Place the wine and eschalot in a saucepan over medium-high heat. Bring the mixture to a boil then reduce the heat to medium-low and reduce the liquid down by about half, about 4 minutes. Remove from heat and set aside.
Place the Parmesan cheese, garlic and walnuts into a food processor; process until finely chopped. Add the olive oil, coriander and 1/8 teaspoon black pepper; process until smooth. Remove the coriander pesto from the food processor and set aside.
Place the capsicums into the food processor, pour in the wine reduction and process until smooth. Pour the entire mixture back into the saucepan and bring to a boil over medium-high heat. Reduce the heat to medium and simmer the sauce for 4 minutes. Meanwhile, season both sides of the tuna fillets with salt and pepper.
Cook the fish on the barbecue until the fish is golden and flakes easily with a fork, about 4 minutes per side.
Whisk the butter, 1/8 teaspoon black pepper and 1/4 teaspoon salt into the red capsicum sauce until smooth. Spoon the sauce onto the bottom of the serving plate, arrange the fish on the sauce and top with the coriander pesto to serve.