Bring a pot of salted water to a boil and cook the chickpea pasta according to package directions, reserving 2 tablespoons of the pasta water before draining.
While the pasta cooks, cut the chicken breast into bite-sized pieces and season with sea salt, black pepper, and dried oregano.
Heat the olive oil in a large skillet over medium-high heat and add the chicken, cooking until golden brown and cooked through, about 5-7 minutes.
Reduce the heat to medium and add the minced garlic, sautéing for 1 minute until fragrant.
Add the baby spinach to the skillet and stir until just wilted.
In a small bowl, whisk together the Greek yogurt, nutritional yeast, and the reserved pasta water until smooth.
Remove the skillet from the heat and stir in the cooked pasta and the yogurt mixture, tossing until everything is evenly coated in the creamy sauce.
Garnish with freshly chopped parsley and serve immediately.