Pat the steaks dry thoroughly. Wrap tightly in plastic wrap and freeze just until firm enough to slice, 20 to 30 minutes. In a large bowl, whisk together the tamari, rice vinegar, shaoxing, honey and arrowroot mixture until well combined.
Slice the steak as thinly as possible against the grain. Add to the bowl with the tamari mixture and stir to coat. Let stand at room temperature for 30 to 60 minutes.
Place a large skillet or wok over medium-high heat until hot. Add a tablespoon of avocado oil and the mushrooms. Season lightly with salt and pepper and cook, stirring, until the mushrooms release their water and begin to turn golden, 5 to 7 minutes. Add the broccoli, season lightly with salt and pepper and cook, stirring, until just tender and bright green, 2 to 3 minutes. Add the bell pepper, scallions, garlic and ginger; cook, stirring, until fragrant, 1 to 2 minutes.
Add the remaining tablespoon of avocado oil; swirl to coat the bottom of the skillet. Add the steak and marinade and cook, stirring constantly, until the meat is just cooked through and the sauce thickens, 2 to 3 minutes. Remove from the heat and drizzle with the sesame oil.
Divide the stir fry among 4 shallow bowls, sprinkle with cashews and serve with rice or noodles, if desired.