Trim any large fat ribbons from beef chuck roast. Cut beef into thin bite-size cubes or strips.
2. In Instant Pot ( pressure cooker ) insert, add 3 tablespoons oil. Turn Instant Pot "ON" then press "SAUTEE". Sautee beef chunks in 3 batches over medium heat, flipping once to brown each side. Place browned beef in bowl.
3. To make the Beef and Broccoli sauce, whisk together beef broth, soy sauce, brown sugar, black pepper, minced garlic, rice vinegar, and red pepper flakes.
4. Pour sauce into pressure cooker. Scrape the bottom to remove any beef pieces until clean.
5. Add in remaining sauteed beef and its juices.
6. Secure lid. Set the pressure valve to SEALING. Select "MANUAL" or "PRESSURE COOK"; use the arrows to cook on high-pressure 17-20 minutes.
7. Cut broccoli florets into bite-size pieces. Place in a microwave-safe bowl with 3/4 cup water. Cover top of bowl with a microwave-safe plate. Place in microwave and cook 6-7 minutes.
8. In a medium saucepan, bring water to boil. Add in rice noodles. For thin angel hair rice noodles, cook 5-6 minutes. For thick lo-mein style noodles, cook 10 minutes or until soft. Drain water and rinse under cold water to remove starches.
9. Once Instant Pot is done, Select "CANCEL". Quick-Release (QR) steam pressure knob. Once pressure pin drops, open lid.
10. In a small bowl, mix 3 tablespoons cold water into 3 tablespoons corn starch. Stir until smooth then add the slurry to the beef.
11. Select " SAUTEE" and stir sauce until it thickens; about 2-4 minutes. Once done, turn "OFF" device.
12. Drain steamed broccoli from bowl then stir into beef sauce.
13. Serve over rice noodles or rice.