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Whisk together mayonnaise, Sriracha, ketchup, rice vinegar, sugar, garlic powder, and salt for the Yum Yum Sauce in a small bowl until smooth and well combined. Cover and refrigerate until ready to use.
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Whisk together soy sauce, brown sugar, sesame oil, water, and garlic in a bowl; set aside.
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Bring a large saucepan of water to a boil over medium-high heat. Add yakisoba noodles and cook for 1 minute. Drain and set aside to cool slightly.
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Heat oil in a wok or large skillet over medium-high heat. Add broccoli and cook until softened and lightly browned, 3 to 4 minutes. Remove from wok using a slotted spoon and set aside.
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Add butter to the wok. When melted, add chicken in a single layer, working in two batches if necessary. Cook until lightly browned on all sides and cooked through (an instant-read thermometer inserted into the thickest part should read at least 165 degrees F (74 degrees C)), about 5 minutes per batch.
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Pour in soy sauce mixture. Let mixture come to a simmer, and cook until sauce has slightly thickened, about 5 minutes.
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Add broccoli and noodles to the wok. Toss until everything is evenly coated in sauce and heated through.
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Garnish with green onions and sesame seeds. Serve with Yum Yum sauce.