Step one: Prepare the sauce
Core the tomatoes and bring a large pot of water to a boil. Prepare a large ice bath with more ice than water. Blanch the tomatoes in the boiling water for 5 seconds and transfer to the ice bath to stop cooking. Once they have cooled, peel the skins from the tomatoes and discard. Cut the tomatoes in half lengthwise and scoop out the centers into the donabe. Divide the tomato halves into 2 pieces each and cut away the interior of the tomato from the outer flesh using a paring knife. Place the interior of the tomato in the donabe. Reserve the exterior of the tomatoes, that will now resemble petals. Place the donabe over medium heat and bring the tomato centers to a simmer. Simmer uncovered for about 1 hour, stirring regularly and scraping down the sides.
Meanwhile, preheat the oven to 275°F (135°C). Line a baking sheet with parchment paper or a silicone baking mat and lay the tomato petals, insides up, in a single layer on the sheet. Sprinkle with a little salt and lay one slice of garlic on each petal. Drizzle with the olive oil and place in the oven. Turn the tray every 15 minutes, until the tomatoes are dry but still jammy (tomatoes should bake for a total of about 45 minutes). Set aside to cool.
Bring a pot of water to a boil and blanch the greens briefly until just tender, 5 to 10 seconds. Drain in a colander and allow to cool at room temperature. Sprinkle with a small amount of salt.
Once the tomato sauce has cooked down to a sauce consistency and is beginning to concentrate, prepare the fish. In a sauté pan, heat the oil over medium-high heat. Place the fish skin-side down in the pan and sprinkle with salt. Cook on the skin side only until crisped and just cooked through, about 1 minute. Transfer to paper towels to drain.
Cut the cherry tomatoes into quarters. Taste the sauce and season with salt if needed; gently fold in the cherry tomatoes, dried tomatoes, and greens (reserving some of each to place on top). Cut the fish into strips about 3 inches (7.5 centimeters) long. Combine with the sauce and garnish the top with greens, dried tomatoes, fresh tomatoes, yuzu zest, and chrysanthemum petals.