Preheat the oven to 350 degrees F. Cut about ½ of the squash into organically shaped, 1 inch chunks. Add to a large mixing bowl. Cut the cherry tomatoes in half and add to the bowl. Quarter and cut the shallots into quarters, peel into petals, and add to the bowl. Roughly tear and add the red chile to the bowl.Season the vegetables with salt and pepper. Add the fresh lemon zest and half of the juice from 1 lemon. Drizzle half of the olive oil over the vegetables. Splash the white wine over the vegetables. Finish by scattering the fresh herbs over the vegetable mixture, reserving a few leaves of each herb for garnish.Gently mix the vegetables and spread them out on a rimmed baking tray. Slide the tray into the preheated oven. Roast for about 8 minutes, to start.
While the vegetables are roasting, prepare the trout fillets. If you're using whole butterflied trout, remove the head and tail. Trim the inner belly and cut the fish into two fillets. Season the trout fillets with salt on both sides, and pepper on the flesh side only. Drizzle some of the remaining olive oil on the skin.
Heat a heavy duty skillet over medium-high heat. Drizzle in a little olive oil. To prepare the salad for the fish, trim the remaining squash and shave into very thin slices, preferably on a Japanese mandolin. Season the squash ribbons with salt, lemon and a little drizzle of olive oil.Once the pan is hot, gently lay the trout fillets skin side down in the pan. Gently press the skin into the pan, to get an even sear on the fish. After the fish has begun to turn opaque on the sides and the skin has released from the pan, the fish is ready to go into the oven. Remove the vegetables from the oven, and lay the fillets, flesh side down, over the top. Return the tray to the oven, to roast for a few more minutes. The squash should be bright in color and barely cooked, with a bit of toothiness.
Remove the tray from the oven and divide the cooked vegetables evenly among 2 warm plates. Place a fillet atop each bed of vegetables and scatter each plate with a few squash ribbons, extra torn herbs and a drizzle of olive oil. Serve immediately.