Heat the olive oil in a large skillet over medium heat. Once hot, add the minced garlic and grated ginger, sauté for 1-2 minutes until fragrant.
Add the fresh broccoli florets to the skillet and pour in the chicken broth. Cover and steam the broccoli for about 3-4 minutes, or until it’s bright green and tender-crisp.
Uncover the skillet and push the broccoli to one side. Add the shrimp to the empty side of the skillet. Season them with salt, pepper, and red pepper flakes, if using. Cook for about 2-3 minutes until the shrimp turn pink and opaque.
Pour the soy sauce and sesame oil over the shrimp and broccoli. Gently toss everything together in the skillet to combine the flavors and heat through for another 2 minutes.
Remove from heat and garnish with chopped green onions and sesame seeds before serving.