Cook the chickpea pasta in a pot of boiling salted water according to package directions, reserving 0.25 cup of the pasta water before draining.
Season the chicken breast evenly with half of the sea salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat and sear the chicken until golden brown and cooked through, then remove from the pan to rest.
Lower the heat to medium-low and add the minced garlic to the same skillet, sautéing for 1 minute until fragrant.
In a small bowl, whisk together the Greek yogurt, parmesan cheese, and the reserved pasta water until a smooth sauce forms.
Pour the yogurt mixture into the skillet and add the baby spinach, stirring constantly until the spinach is just wilted.
Slice the rested chicken into strips and return it to the skillet along with the cooked pasta, lemon juice, remaining salt, pepper, and red pepper flakes, tossing to coat everything in the sauce.