Add the butter into the insert of the Instant Pot and turn on the sauté function. Once melted, add in the finely diced onion, salt, and pepper. Let it cook, while stirring constantly, until softened. About 3-5 minutes.
3 tablespoons unsalted butter, 1 small yellow onion, 1 teaspoon kosher salt, ½ teaspoon black pepper
Stir in the garlic and cook for 1 minute, while stirring constantly, until the garlic is fragrant. Turn off the sauté function and scrape the bottom of the instant pot to remove any stuck on food bits.
3 garlic cloves
Stir in the chicken broth, broccoli florets, and matchstick carrots.
1 box (32 oz) chicken broth, 4 cups chopped broccoli florets, 1½ cups matchstick carrots
Close the lid and ensure the Instant Pot lid is locked in and the vent is in the 'sealed' position. Cook on HIGH pressure for 1 minute.* It will take about 8 minutes to come up to pressure and then the 1 minute cook time will start. While the soup is cooking stir together the cornstarch slurry by mixing the water and cornstarch with a fork. Set aside.
1/4 cup cold water, 1/4 cup cornstarch
When the instant pot beeps (the timer is done) do a quick pressure release of the steam (move the valve to the 'venting' position) and release all the steam.
Slowly add in handfuls of the shredded cheeses while stirring constantly.
2 cups shredded cheddar cheese, 2 cups shredded Colby Jack cheese
Turn the sauté function back on and pour in the heavy cream and cornstarch slurry. Mix and stir it well until the soup is bubbly and thickened. About 2-3 minutes.
2 cups heavy cream