Prepare the zucchini: using a zoodle maker or vegetable peeler, make zoodles from the 2 large zucchini and set aside.
Heat 1 tablespoon butter in a large skillet over medium-high heat until melted and shimmering.
Add the 1 1/2 lb chicken thigh strips to the hot pan and sprinkle with a pinch of salt; pan-fry, turning occasionally, until golden brown and cooked through, about 6–8 minutes depending on thickness.
Add the chopped fresh semi-dried tomato strips and chopped jarred sun-dried tomatoes to the pan along with 1 tablespoon of oil from the jar if desired, then add the crushed garlic and sauté until fragrant, about 1 minute.
Reduce the heat to low, pour in 1 1/4 cups thickened cream and stir to combine.
Stir in 1 cup shaved Parmesan until melted and smooth, then season with the remaining pinch of salt, 1 teaspoon dried basil, and 1/2 teaspoon red chilli flakes; taste and adjust seasoning if needed.
Add the zucchini zoodles to the skillet and toss gently to coat in the sauce; simmer over low heat until zoodles reach your desired tenderness, about 5–8 minutes.
Serve immediately while warm.