Place the oven rack in the middle of the oven. Preheat the oven to 450 degrees F. Place the lemongrass tops along the bottom of the baking dish. Arrange the reserved green onion (white parts) over the lemongrass.
Spoon half the tomato sauce, including the lemongrass stalks, over the green onion (white parts).
Oil the fish pieces, and season with salt and pepper. Place the fillet pieces over the tomato sauce, skin-side up. Place the chopped lemongrass bottoms inside the slits of fillet pieces. Spoon the remaining sauce over the snapper. Bake the fish in the oven until the snapper is cooked through, approximately 15 minutes. Garnish with the reserved chopped green onion tops. Serve with the Ginger Buttered Potatoes and Broccoli with Crispy Garlic.
Heat the oil in a large, wide-based pot over medium heat. Add the shallots, garlic and lemongrass stalks. Saute until the shallots and garlic are slightly golden. Deglaze with white wine. Reduce by 2/3 over high heat, approximately 1 to 2 minutes. Add the tomatoes, stir and cook for 15 minutes. Remove from the heat, add the lemon zest and season with salt.
Heat the butter over low heat in a small pot. Add the ginger and whisk together. Transfer to a bowl and place in freezer. After 5 minutes, whisk again and return to the freezer for 5 to 10 minutes until the butter has solidified. Place a large piece of plastic wrap on board. Spread the ginger butter in the center of the plastic wrap. Roll the plastic wrap over the ginger butter and twist the ends, creating a log. Place the ginger butter in the refrigerator.
Place the ginger butter in a saute pan over low heat. Once the ginger butter has melted, add the potatoes to the pan. Toss until the potatoes are warmed and are coated with ginger butter, approximately 5 minutes. Remove from heat and season with salt.
Heat the oil in a saute pan over medium heat. Place the garlic in the pan, fry until crispy, tossing constantly, approximately 5 minutes. Add the broccoli, toss to incorporate and remove from the heat. Season with salt.