Use your pressure cooker's saute function to melt the vegan butter or heat the olive oil. Add the onion and garlic and cook, stirring, until the onion becomes translucent, just a few minutes.
Press the cancel button, then add the carrots, potato, broccoli, water and broth cubes. Cook at high pressure for 5 minutes with a 10-minute natural release.
Use an immersion blender to puree the soup. If you don't have an immersion blender, you can do this in an upright blender, but don't blend the soup while it's still boiling hot! Let it cool for a bit.
Add the vegan milk and cheddar shreds to the potful of soup, and press the saute button. Cook, stirring until the cheese melts. Season with salt and pepper and serve.
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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.