In a large skillet, heat the olive oil over medium heat until shimmering. Add the finely minced garlic and grated ginger to the skillet, stirring frequently. Sauté for 1-2 minutes until the mixture is fragrant and the garlic is lightly golden.
Introduce the fresh broccoli florets to the skillet and pour in the low-sodium chicken broth. Cover the skillet with a lid and allow the broccoli to steam for approximately 3-4 minutes, or until it becomes a vibrant green and retains a tender-crisp texture.
Once the broccoli is cooked, remove the lid and gently push the florets to one side of the skillet. Place the peeled and deveined shrimp on the opposite side. Season the shrimp generously with salt, freshly ground pepper, and red pepper flakes, if desired. Cook the shrimp for about 2-3 minutes, flipping occasionally, until they turn pink and opaque, indicating they are cooked through.
Drizzle the soy sauce and sesame oil over both the shrimp and broccoli in the skillet. Gently stir everything together, ensuring that the flavors meld, and cook for an additional 2 minutes to heat through.
Remove the skillet from heat. Before serving, garnish the dish with the finely chopped green onions and a sprinkle of toasted sesame seeds for a delightful crunch.
Notes
Serve in a colorful shallow bowl with lemon wedges for added brightness.