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In a large skillet heat olive oil over medium high heat and add minced garlic and the chicken. Pour sesame oil over the chicken and cook for around 3-4 minutes, until the chicken is no longer pink.
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Add broccoli florets to the skillet and cook for another minute. Add 1/2 cup chicken broth to the skillet with broccoli and soy sauce. Cover and cook for about 3 minutes, until broccoli is tender.
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Add cornstarch if you prefer a thicker sauce and continue to let simmer until the sauce has thickened. Serve with sprinkled sesame seeds.