Press 'SAUTE' button, and set it to 'NORMAL'. Once it displays 'HOT', add butter, let it melt. You can also add a tablespoon of oil, to prevent the butter from burning. Add diced onions along with minced garlic. Saute until the onions turn translucent and the garlic is fragrant.
Add salt, white or black pepper, and ground mustard. You may also add 1/4 - 1/2 tsp of red pepper flakes or cayenne pepper for some heat. Saute for another 30 seconds.
Deglaze the browned bits of butter with 1/2 cup of vegetable stock.
Add carrots, broccoli, and stock, Mix well to combine.
Press 'CANCEL'. Close the lid of the Instant Pot. Set the valve to 'SEALING'. Pressure cook on high for 2 minutes. It will take some time for the pressure to build up (about 8 minutes), after which the timer will begin.
Mix the cornstarch with the cream and set it aside.
Do a quick release of the pressure as per the manufacturer's instructions. Once the silver pin drops, turn the knob to 'VENTING' and open the lid away from you.
Use an immersion blender to puree the soup, leaving it chunky or smooth as per your desired consistency. You may also transfer the contents into a jar of the blender to one-half full and blend. Exercise precaution when blending hot liquids.
Press the 'CANCEL' button and turn on the 'SAUTE' button. Once the soup begins to bubble, add the cornstarch mixture (whisk it again before pouring as cornstarch settles dowand keep stirring the soup until it thickens. Press 'CANCEL' to turn off the 'SAUTE' mode.
Add 1 cup of shredded cheddar cheese. Mix well until all the cheese has melted. Then add the remaining cup of cheese, stir it in until well combined and creamy.
Add freshly grated nutmeg, and mix well. Check for seasoning and adjust with more salt and pepper as desired. Dish out and serve fresh, homemade broccoli and cheese soup. Top with more shredded cheese, croutons or any of your favorite toppings. Refrigerate leftovers in an airtight container up to 3 days.