Heat ½ tbsp olive oil in a large pan or wok over medium heat. Add the diced chicken, season with salt and pepper, and cook for 6-8 minutes until browned and fully cooked. Remove and set aside.
Add the remaining ½ tbsp olive oil to the pan. Add the shrimp, season lightly, and cook for 2-3 minutes per side until pink and opaque. Remove and set aside with the chicken.
In the same pan, add the garlic and ginger, cooking for about 1 minute until fragrant.
Add the bell peppers, zucchini, and broccoli. Stir-fry for 4-5 minutes until the vegetables are tender yet crisp.
Return the chicken and shrimp to the pan and pour in the soy sauce and lime juice, stirring to coat everything evenly.
Add chili flakes for extra heat if desired, and cook for an additional 2-3 minutes to allow the flavors to meld together.
Garnish with sesame seeds before serving.