Bring a large saucepan of water to a boil. Add the broccoli and cook until bright green and tender-crisp, about 2 minutes. Drain and set aside.
Heat the canola and sesame oils in a large nonstick skillet set over medium heat. Add the onions, ginger, garlic and chiles and saute until the onions are soft, 3 to 5 minutes. Increase the heat to medium-high, add the chicken and cook, stirring occasionally, until the chicken is cooked through, 5 to 7 minutes. Transfer to a plate.
In a small bowl, whisk the cashew butter and tamari and pour into the skillet, stirring to remove any lumps. Add the chicken back in the pan, stir in the broccoli and cashews, and stir to heat through and completely coat with the sauce. Season with salt and pepper, then serve.
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