Boil the pasta. Bring a large pot of salted water to a boil, cook the high-protein pasta according to package directions until al dente, then drain while reserving about 1/2 cup of the pasta water.
Prep the lemon and yogurt mix. While the pasta cooks, zest the lemon, then juice it, and in a small bowl whisk together the Greek yogurt, chicken broth, lemon zest, lemon juice, and cornstarch until smooth.
Season the chicken. Pat the chicken pieces dry with a paper towel, then season them with the salt, black pepper, and red pepper flakes if using.
Sear the chicken. Heat the olive oil and butter in a large skillet over medium-high, add the chicken in an even layer, and cook for 5–7 minutes, stirring occasionally, until golden and cooked through.
Add garlic and spinach. Turn the heat down to medium, stir in the minced garlic and chopped spinach, and cook for 1–2 minutes until the garlic is fragrant and the spinach just begins to wilt.
Create the creamy lemon sauce. Reduce the heat to low, pour the lemon-yogurt mixture into the skillet, stirring constantly for 1–2 minutes so it gently warms and thickens without boiling.
Toss in the pasta. Add the cooked pasta and 2 tablespoons of reserved pasta water to the skillet, sprinkle in the Parmesan, and toss everything together until the pasta is evenly coated and the sauce is silky, adding more pasta water a splash at a time if needed.
Taste and serve. Taste and adjust salt, pepper, or extra lemon juice as needed, then remove from heat and serve immediately topped with chopped parsley if you like.