You'll have more green sauce than you'll need for this recipe, but it will keep in the refrigerator at least a week. Spoon it on steak, chicken, pasta, or roasted vegetables.
In a large saucepan, cover 2 pounds small red new potatoes (about 21) with cold water; season with coarse salt. Bring to a boil, reduce to a simmer, and cook just until tender when pierced with a paring knife, about 15 minutes. If saving for another day, drain and let cool; then cover and refrigerate for later use.
Preheat oven to 475 degrees. Lightly oil a rimmed baking sheet. Smash each potato with the base of your palm and place on sheet. Drizzle with 2 tablespoons oil; season with salt and pepper. Roast until crisp, about 20 minutes.
Make green sauce. Chop remaining mint and basil and 1 bunch fresh parsley leaves. In a bowl, combine with 1 garlic clove, minced, and 1 tablespoon chopped capers. Stir in 1 tablespoon fresh lemon juice and enough extra-virgin olive oil to coat; season with coarse salt and ground pepper. If saving for another day, cover and refrigerate for later use.
Make roasted tomatoes. Reduce oven heat to 350 degrees. Halve 14 plum tomatoes. On 2 large rimmed baking sheets, arrange tomatoes, cut side up, and sprinkle with 1/2 teaspoon sugar. Bake until softened and edges are crinkled, about 1 hour. If saving for another day, let cool. Cover and refrigerate for later use.
Meanwhile, score fish skin in a few places with a paring knife and season fillets with salt and pepper. In a large nonstick skillet, heat 1 tablespoon oil over medium-high. Add fish, skin side down, and cook until browned and crisp, 6 to 8 minutes. Reduce heat to medium; flip fish and cook until opaque throughout, 2 to 4 minutes. Serve fish with green sauce, potatoes, and tomatoes.