Start by turning your Instant Pot to sauté mode. Add olive oil and butter. Once melted, toss in the minced onion and shredded carrot. Let them cook for about 3 to 4 minutes until soft and golden. This builds a sweet, buttery base that makes the soup rich in flavor. While this cooks, chop your broccoli into small florets so they cook evenly.
When the onion and carrot are ready, hit “Cancel” to stop sautéing. Pour in about 2¾ cups of chicken stock, saving the rest for later. Use a spoon to scrape the bottom of the pot so no bit’s stick. Add the salt, pepper, and garlic powder, then drop in the broccoli florets.
Close the lid, set the vent to “Sealed,” and cook on manual for 0 minutes. Yes, zero minutes! It just needs to come to pressure to steam the broccoli until tender. Once it finishes, let the soup sit for 5 minutes, then do a slow release of the steam. Open carefully because it is extremely hot.
After opening the lid, turn the Instant Pot back into sauté mode. Mix the leftover chicken stock with cornstarch in a bowl until smooth. Pour this into the soup while stirring. In 2–3 minutes, you will see it thicken into a creamy base.
Lower the heat and stir in half and half. Slowly sprinkle in the grated cheddar cheese, stirring until it melts completely. Make sure you stir gently so the cheese blends smoothly without clumping.
Put the lid back on, but do not seal it, and let the soup sit for 2–3 minutes. This helps the cheese settle in fully. Give it one last stir, then ladle into bowls and serve warm.