Boil a large pot of salted water and cook the pasta according to package directions until al dente, reserving 1/4 cup of pasta water before draining.
Season chicken cubes with salt, pepper, and oregano.
In a large skillet over medium-high heat, cook chicken until browned and the internal temperature reaches 165°F (74°C). Remove chicken and set aside.
Reduce skillet heat to low and sauté minced garlic for 1 minute until fragrant.
Whisk together Greek yogurt and chicken broth, then add to the skillet, stirring constantly to ensure a smooth consistency without curdling.
Integrate the cooked pasta, chicken, and spinach into the skillet, tossing until the spinach is wilted.
Fold in parmesan cheese and red pepper flakes, adding reserved pasta water if necessary to adjust sauce viscosity.
Divide into four equal portions for immediate service or meal prep storage.