Combine the onion, carrots, cauliflower, broccoli, mustard, water, and 2 teaspoons salt in the Instant Pot. Secure the lid and move the steam release valve to Sealing. Select Manual/Pressure Cook to cook on high pressure for 3 minutes.
When the cooking cycle is complete, immediately move the steam release valve to Venting to quickly release the pressure. When the floating valve drops, remove the lid. Use an immersion blender to blend the soup, leaving as much texture as you like.
Add the Cheddar, Parmesan, and almond milk and stir until combined. Season with salt and pepper to taste, then serve warm. Store leftovers in an airtight container in the fridge for 5 days.