Set your pressure cooker to sauté and add the olive oil, diced onions, chopped carrots, and chopped broccoli stems. Cook stirring frequently for 4-5 minutes until softened but not browned.
Add the thyme sprigs, diced garlic, and red pepepr flakes, allow to sauté for 1-2 minutes until fragrant.
Deglaze the pot with the broth and scrape any browned bits with a wooden spatula. Drain and add the cans of beans and add the can of diced tomatoes. Stir in the uncooked barley and place the lid on the pressure cooker.
Pressure cook on high for 6 minutes and administer a quick release. Promptly add the broccoli florets to the boiling soup, then top with the chopped kale. Place the lid back on the pot for 5 minutes to let the broccoli cook and the kale to wilt.
Taste the broth and adjust the salt to taste. Add some fresh cracked pepper.
Serve in bowls and sprinkle optional parmesan cheese.