Use your pressure cooker's sauté function to melt the vegan butter or heat the olive oil. Add the onion and garlic and a pinch of salt, then cook, stirring, until the onion becomes translucent, just a few minutes.
Press the cancel button, then add the broccoli, carrots, broth, salt, pepper, paprika, and mustard powder.
Lock the lid and cook at high pressure for 0 minutes with a 10-minute natural release. Press the cancel button.
Add the vegan milk and cheddar shreds to the potful of soup, and press the sauté button again. Slowly add the cornstarch-water mixture, and cook, stirring frequently, until the soup thickens to your preference.
Season to taste with more salt and pepper. You can also add a little cayenne, if you like a little heat, or more mustard powder, if it needs more tang. Serve hot.
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Notes
Leftovers will keep for 3 to 5 days in the refrigerator. You can warm it back up on the stovetop or in the microwave. It will keep for up to 3 months in the freezer. That overnight in the fridge or on the kitchen counter for a couple of hours, then warm in the microwave or on the stovetop. Make sure to stir when you warm it up, because freezing can cause the soup to separate a bit.If you like your broccoli cheddar soup to be creamier, you can use an immersion blender to puree some or all of the veggies after cooking at pressure.