Combine the ingredients for the marinade (soy sauce, olive oil and hot sauce) in a shallow plate or bowl. Add the steak strips into the marinade and allow to marinate in the refrigerator for 30 minutes to one hour.
In the meantime, wash and break down the broccoli heads into florets. Blanch the florets into boiling water for 1 or 2 minutes, then rinse with cold water.
Bring the steak to room temperature and heat oil and one tablespoon butter in a large skillet over medium-high heat — reserve the juices of the marinade for later. Sear the steak strips in batches for 1-2 minutes each side until edges are crispy and browned, adding extra oil if needed. Remove the steak strips from the skillet and set aside to a plate.
Using the same skillet, lower the heat to medium. Melt 2 tablespoons butter, then add lemon juice, minced garlic, beef broth, and remaining marinade juices. Bring to a simmer then stir in the fresh parsley and broccoli florets and toss regularly until the sauce a reduced and the broccoli is cooked to your liking.
Add the steak strips back to the pan to reheat quickly. Serve immediately with thyme, chili flakes, more parsley, and lemon slices.