Bring a large pot of salted water to a boil. Add chickpea pasta and cook according to package directions until al dente. Reserve 1/4 cup pasta water, then drain and set aside.

While pasta cooks, season chicken pieces with garlic powder, salt, and pepper. Heat 2 teaspoons olive oil in a large skillet over medium-high heat. Add chicken in a single layer and cook for 5-6 minutes, stirring occasionally, until golden and cooked through (165°F internal). Transfer to a plate.

In the same skillet, reduce heat to medium. Add the remaining 1 teaspoon oil and butter. Sauté minced garlic for 30 seconds until fragrant. Take skillet off heat and let cool 1 minute. Stir in room-temperature Greek yogurt, Parmesan, and reserved pasta water until smooth and creamy. Return to low heat and warm gently, stirring constantly (do not boil).

Add cooked pasta, chicken, and spinach to the sauce. Toss over low heat until spinach wilts and everything is well-coated, about 2 minutes. If sauce is too thick, thin with a splash more pasta water.

Divide among bowls, garnish with parsley, extra Parmesan, and a pinch of red pepper flakes. Serve immediately.