Preheat the oven to 200°F (93°C). Line two baking sheets with paper towels.
Spiralize the zucchinis using a 3 mm blade. Divide the noodles evenly between the prepared baking sheets in a single layer and sprinkle lightly with salt.
Bake the zucchini noodles for 40 minutes to dry them. After baking, cover with fresh paper towels and press gently to absorb moisture; repeat with another towel if needed. Set the dried noodles aside.
Increase the oven temperature to 375°F (190°C). In a large saucepan over medium-low heat, combine the Greek yogurt, 1/2 cup BBQ sauce, and 1 cup of the grated cheddar. Cook, whisking regularly, until the cheese begins to soften and the sauce becomes melty, about 8–10 minutes. Do not overcook the yogurt.
In a large bowl, toss together the shredded chicken, chopped cilantro, and the dried zucchini noodles. Lightly chop the mixture with a fork and knife so it mixes evenly and is easier to serve once baked.
Pour the warm yogurt-BBQ-cheese sauce over the zucchini and chicken mixture. Season with a pinch of pepper and mix until everything is evenly coated.
Spread the mixture into a casserole dish in an even layer. Bake for 20 minutes.
Remove from the oven, sprinkle with the remaining 1/2 cup grated cheddar, then return to the oven and bake until the top is golden and bubbling, about 20–25 minutes more.
Let the casserole rest for 20 minutes to set and allow any excess liquid to be absorbed. Cut into portions, drizzle with additional BBQ sauce and garnish with cilantro if desired, then serve.