Whisk together 1/4 cup lime juice, garlic powder, cumin, salt and pepper in a large bowl; add the chicken breasts. Cover and refrigerate 1 to 2 hours, turning the chicken occasionally.
Preheat an oven to 220 degrees C.
Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Once the water is boiling, stir in the linguine and return to a boil. Cook the pasta uncovered, stirring occasionally until the pasta has cooked through but is still firm to the bite, about 11 minutes. Drain well in a colander set in the sink.
Transfer linguine to a large mixing bowl; add 2 tablespoons olive oil, the Parmesan cheese and the quartered cherry tomatoes; toss until the pasta is evenly coated in oil.
Heat 1 tablespoon olive oil in a frypan over medium heat. Cook the chicken breasts, turning once, until no longer pink in the centre and the juices run clear, about 20 minutes.
Meanwhile lie the zucchini on a baking tray. Coat the zucchini with 1 tablespoon olive oil with a pastry brush. Place zucchini on middle rack in the oven and bake, turning every 5 minutes until nicely browned, 15 to 20 minutes.
Melt the butter in a saucepan over medium heat. Add the coriander and garlic, cook and stir 1 minute. Pour in the wine, chicken stock and 2 tablespoons lime juice then return to a simmer. Transfer the mixture to a blender and blend until smooth. Return the mixture to the sauce pan and stir in the cream and spring onions; bring to a boil and remove from heat.
Lie the zucchini pieces side by side on a serving platter; lie the chicken breasts on the zucchini; pour the coriander cream sauce over the chicken. Serve with the pasta on the side.