In a medium saucepan, bring chicken broth to a boil. Add orzo, reduce heat to low, cover, and simmer for 10 minutes or until liquid is absorbed. Stir in butter and parsley.
Season chicken breasts with salt and pepper. Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Sear chicken for 6-7 minutes per side until the internal temperature reaches 165°F (74°C).
Whisk together balsamic vinegar, honey, mustard, and minced garlic in a small bowl. Pour the mixture into the skillet with the chicken. Simmer for 3-5 minutes until the sauce reduces to a thick glaze.
While chicken finishes, heat remaining 1 tablespoon olive oil in a separate pan over medium heat. Add sliced garlic and cook for 1 minute until fragrant. Add spinach and sauté until just wilted.
Divide the orzo and spinach among four plates. Place one chicken breast on each plate and drizzle with the remaining balsamic glaze from the skillet.