Slice the 1½ pounds sirloin steak against the grain into thin strips and place them in a large bowl.
Add to the bowl: 3 cloves minced garlic, 1 sliced onion, 1 tablespoon lemon juice, ½ tablespoon Worcestershire sauce, ½ teaspoon beef bouillon granules, 1 teaspoon dried thyme, 1½ teaspoons dried oregano, ¼ teaspoon crushed red pepper flakes (optional), and kosher salt and freshly ground black pepper to taste. Toss to coat the steak strips.
Cover the bowl with aluminum foil and marinate at room temperature for 30 minutes.
After marinating, heat a large skillet over high heat until very hot. Add the 2 tablespoons vegetable oil and swirl to coat the pan.
Remove the steak strips from the marinade, letting excess marinade drip back into the bowl. Sear the steak strips in batches in the hot skillet (do not overcrowd) until browned at the edges, about 1–2 minutes per side. Transfer seared strips to a plate and continue with remaining steak.
Pour the reserved marinade from the bowl into the skillet. Bring it to a boil over high heat, then reduce to a simmer and cook for 1–2 minutes to cook off raw juices and slightly reduce the sauce.
Reduce heat to medium, add the 2 tablespoons unsalted butter to the skillet and let it melt. Add the 1 pound broccoli florets and toss to coat in the sauce and butter. Cook, stirring occasionally, until the broccoli is tender-crisp and the sauce has reduced to your liking, about 5–8 minutes.
Return the seared steak strips to the skillet with the broccoli, toss to combine, and cook just until the steak is reheated, about 1–2 minutes. Taste and adjust salt and pepper if needed.
Serve the steak and broccoli over the 3 cups cooked white rice.