Prepare a large bowl of ice water. Fill a medium pot with about 4 quarts water and bring to a simmer over medium heat. Add a generous handful of salt. (The water should taste like sea water.) When the water boils, add the asparagus and cook for 2 minutes. Drain with a slotted spoon or strainer and plunge into the ice bath. Remove to paper towels and pat dry. Set aside.
Heat a large skillet over medium-high heat. Sprinkle the fish with salt and pepper. Add some oil and bring to lightly smoking, then place the fish in the skillet skin-side down. Cook until the skin is crispy, 6 to 7 minutes, then flip to the other side and cook for 3 to 4 minutes more. (If the skillet is getting too hot, reduce the heat.) Remove from the heat and top the skin side with the chopped herbs and salt.
Mix the diced tomatoes with the drizzle of honey, salt and pepper in a small bowl. Set aside.
Remove some of the grease from the skillet. Add the shallots, salt and white wine to the skillet and bring to a boil. Add the butter and cook until the sauce thickens, then drop the dried asparagus into the sauce. Season with salt, pepper and lemon juice. Toss to coat the asparagus.
Place the lemon segments and tomatoes around each of 2 plates. Top with the asparagus, a spoonful of sauce and then the fish (skin-side up). Garnish with additional fresh herbs.