Heat olive oil in a large skillet over medium-high heat. Season chicken with salt, pepper, garlic powder, and onion powder. Cook 6-8 minutes, turning occasionally, until golden brown and cooked through. Transfer to a plate.
Reduce the heat to medium and melt butter in the same skillet. Add shallot and cook 2-3 minutes, until softened. Stir in garlic and cook 30 seconds, until fragrant.
Add zucchini and season with a generous pinch of salt. Cook for 15-20 minutes, stirring every few minutes, until the zucchini slices are very soft, most of the moisture has evaporated, and they're lightly caramelized in places. Reserve 1 to 1½ cups of the cooked zucchini and set aside.
Meanwhile, bring a large pot of salted water to a boil. Cook pasta until al dente according to the package directions. Reserve 1 cup of the pasta water before draining.
Transfer the remaining cooked zucchini to a blender. Add Parmesan, basil, and lemon zest. Blend until smooth and creamy. If the mixture is too thick to blend smoothly, add 1 tablespoon of olive oil.
Pour the zucchini sauce into the skillet over low heat. Add the reserved pasta water, a splash at a time, stirring until the sauce is smooth. Add the cooked pasta and toss until evenly coated.
Fold in the cooked chicken, reserved zucchini, and sun-dried tomatoes. Toss until warmed through.
Divide among bowls and garnish with toasted pine nuts, freshly grated Parmesan cheese, and fresh basil.