Pat the 2 lbs ribeye steak dry with paper towels and slice into thin 1/4-inch strips about 2 inches long.
Heat a large non-stick skillet over medium-high heat. Add 2 Tbsp avocado oil and 2 tsp toasted sesame oil and heat until the oils shimmer.
Add the sliced steak in a single layer (cook in batches if needed to avoid crowding). Stir-fry, stirring frequently, until the steak is browned and beginning to crisp at the edges, about 4–6 minutes.
Add 1/4 cup liquid aminos (or coconut aminos), 1 Tbsp fresh grated ginger, 4 cloves minced garlic, and 1 Tbsp pure maple syrup if using. Stir to combine.
Continue cooking, stirring frequently, until much of the liquid has reduced, about 1–2 minutes.
Add the chopped florets from 2 large crowns of broccoli, stir to coat with the sauce, then cover the skillet. Cook, stirring occasionally, until the broccoli is crisp-tender, about 3–4 minutes.
Uncover, add the 3 chopped stalks of green onion, toss for 30 seconds to 1 minute to warm and soften, then remove from heat.
Serve immediately with rice, cauliflower rice, or a side of your choice.