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 425 degrees F (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 skillet over medium heat. Cook the chicken breasts, turning once, until no longer pink in the center and the juices run clear, about 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Meanwhile, lie the zucchini on a baking sheet. 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 cilantro and garlic, cook and stir 1 minute.
Pour in the wine, chicken broth, and 2 tablespoons lime juice, and 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 green 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 cilantro cream sauce over the chicken.
