Heat oil in a large pot set over medium-high heat. Add the onions and cook for a few minutes until they're tender and translucent. Stir in the garlic and thyme, cook for 30-60 seconds, until fragrant.
Toss in the potatoes and cauliflower florets. Stir to coat and let cook for 20-30 seconds. Sprinkle with salt and pour in vegetable stock. Bring to a boil, then lower the heat to a simmer, cover the pot and cook soup for 20-30 minutes, stirring occasionally. When potatoes and cauliflower can be easily pierced with a fork, remove the pot from heat.
Using an immersion blender, blend the soup until it’s completely smooth. Return pot back on the stove and whisk in the cream. Allow the soup to warm up, taste to see if it needs more salt and pepper. Keep covered until serving time.
Serve soup with some grated Parmesan and parsley, if desired. A dollop of cream is wonderful too.
Store leftover soup covered in the fridge and eat within two days. Reheat on the stove or in the microwave.