Trim broccoli into bite-size florets (about 3 cups). Wipe mushrooms clean and slice to roughly 1/4-inch thick. Peel the onion and cut into 1/4- to 1/2-inch slices or half-moons. Core and seed the bell peppers, then cut into 1/2-inch strips. Thinly slice the garlic cloves. Slice the pitted black olives if not pre-sliced.

Measure out the soy sauce, lemon juice, dried oregano, red pepper flakes, salt and pepper. Chop parsley and grate Parmesan if using.

Cook

Blanch broccoli (optional for brighter color)

Bring a medium pot of salted water to a boil. Add the broccoli florets and cook for 1 minute until bright green and slightly tender. Immediately transfer to a bowl of ice water to stop cooking. Drain and set aside. (If you prefer firmer broccoli or skip the step, proceed directly to sautéing.)

Sauté aromatics

Heat a large skillet or sauté pan over medium-high heat. Add the olive oil and butter (if using). Once shimmering, add the sliced onion and sauté 3–4 minutes until it begins to soften and turn translucent. Add the sliced mushrooms and continue to cook 4–5 minutes until they release their liquid and start to brown. Add the sliced garlic and cook 30–45 seconds until fragrant, stirring to avoid burning.

Add peppers and broccoli

Add the red and green bell pepper strips and the blanched/drained broccoli to the pan. Toss to combine and cook 3–5 minutes until peppers are tender-crisp and broccoli is heated through.

Season and finish

Reduce heat to medium. Stir in the soy sauce, lemon juice, dried oregano, crushed red pepper flakes, salt, and black pepper. Toss and cook 1–2 minutes so the flavors meld and some liquid reduces. Taste and adjust seasoning (add up to 1/4 tsp more salt or a squeeze more lemon if desired). Stir in the sliced black olives and cook 30 seconds just to warm them.

Serve

Transfer the vegetables to a serving platter. Sprinkle with chopped parsley and grated Parmesan if using. Serve hot as a side dish, over rice, pasta, or mixed into a grain bowl.

Leftovers: store in an airtight container in the refrigerator for up to 3 days. Reheat gently in a skillet or microwave.