Preheat your oven to 400°F and toss the cherry tomatoes with a tiny drizzle of oil on a baking sheet; roast for 12-15 minutes until they begin to burst.
Bring a pot of salted water to a boil and cook the chickpea pasta according to package directions, reserving 0.25 cup of the starchy pasta water before draining.
Season the chicken breast with half of the salt and pepper, then sear in a skillet over medium heat with the olive oil until golden and cooked through, about 6 minutes per side.
Remove the chicken to rest, then in the same skillet, sauté the minced garlic and red pepper flakes for 1 minute until fragrant.
Lower the heat and whisk in the Greek yogurt, parmesan cheese, and the reserved pasta water to create a smooth, creamy sauce.
Slice the chicken and add it back to the skillet along with the cooked pasta, roasted tomatoes, and fresh spinach, tossing until the spinach is just wilted and everything is coated in sauce.
Finish with the remaining sea salt and black pepper before serving immediately.