Combine the beef, peppers, onion, garlic, scallions, jerk seasoning, ginger, and thyme in a bowl. Let sit for 15 minutes.
Heat the olive oil in a non-stick pan over medium heat. Add in the beef strips and sauté until browned. Then add in the remaining ingredients from the bowl. Sauté for 6 minutes, then add in the broth and bring to a simmer for 5 minutes.
Dissolve cornstarch in water and slowly add it to the sauce, remove the lid and simmer until it thickens to a smooth consistency. Adjust the seasoning with salt to taste before serving.