Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function to heat the pot. Add ground beef and season with salt and pepper. Cook and stir until beef is browned and crumbly, about 5 minutes. Add onions and cook until soft and translucent, 2 to 3 minutes. Stir in garlic and cook until fragrant, about 30 seconds.
Deglaze pot with 1/4 cup chicken broth and allow to cook off, about 3 minutes. Stir in remaining 1 cup chicken broth, red pepper, pearl couscous, parsley, soy sauce, and red pepper flakes; stir until well combined.
Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 6 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid. Mix in spinach. Stir, place the lid loosely on the pot, and leave for 5 minutes to allow couscous to absorb the remainder of the liquid. Taste and season with additional salt if desired.