Heat olive oil and garlic in large skillet or pan over medium-high heat. Add chicken, season with salt and pepper, and cook until lightly golden brown.
Add mushrooms and cook for 2 additional minutes.
Add broth, cream, and milk, stirring to mix well. Bring to a simmer, add pasta, and cook until tender (about 15 minutes).
Add spinach, tossing until slightly wilted (about 1 minute). Remove from heat.