Bring a large pot of salted water to a boil and cook chickpea pasta according to package directions until al dente.
While pasta cooks, heat olive oil in a large skillet over medium-high heat.
Season chicken cubes with salt and pepper, then add to the skillet and sear until cooked through, approximately 6 to 8 minutes.
Add minced garlic to the skillet and sauté for 1 minute until fragrant.
Reserve 1/2 cup of pasta water before draining the pasta.
Lower skillet heat to low; add cooked pasta, baby spinach, and Greek yogurt to the chicken.
Gradually stir in the reserved pasta water and parmesan cheese until a creamy sauce forms and spinach is wilted.
Remove from heat immediately to prevent the yogurt from curdling and serve.