Cut the chicken into bite-sized pieces. Turn on the saute function on the Instant Pot. Add the olive oil and sesame oil to the Instant Pot and add the chicken.
While the chicken cooks, cut the peppers into strips and mince the garlic.
Sauté for 2 minutes so the chicken can start to brown. Add the minced garlic and mix well. Cancel saute mode.
Add the chicken broth and soy sauce and mix well. Try to get any of the brown bits off the bottom of the pot.
Close the pressure cooker lid and make sure the lid is set to the sealing position. Set the cooking time to 10 minutes on high pressure.
While the chicken cooks, make a cornstarch slurry. Add one tablespoon of cornstarch to a bowl with one tablespoon of water. The perfect consistency of the cornstarch slurry is when there are no lumps and looks like a creamy sauce.
When the cook time is completed, quick release the pressure. Open the Instant Pot and add the cornstarch slurry. Mix well.
Press the saute setting one more time. Add the broccoli florets and the red pepper strips to the Instant Pot and cover. Sauté for 3 minutes with the lid closed. This will steam the broccoli and keep it crisp, instead of mushy.
After 3 minutes, check the broccoli. The broccoli should be al dente, or with just a little crunch left. If you like your broccoli softer, add an extra minute to the timer. When the broccoli is cooked, mix everything together and serve over rice.