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In a large skillet heat about 1-1/2 tablespoons sesame oil over medium-high heat. Add in the chopped garlic and dried chili flakes; saute for about 1 minute.
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Add in the broccoli florets and 4 tablespoons chicken broth; cover skillet and cook until the broccoli is just crisp-tender (about 2 minutes) transfer to a bowl.
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Add in 1 tablespoon more sesame oil to the skillet.
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Season the chicken strips with salt and pepper and then add to the hot skillet with the green onions; saute until the chicken is cooked through (about 3 minutes).
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Add in the remaining 2 tablespoons chicken broth, hoisin sauce and oyster sauce. Add in the broccoli florets back to the skillet; toss to combine until heated through (about 1-2 minutes).
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Transfer to a platter or large bowl and sprinkle with sesame seeds.