Heat oven to 425.
Toss the cauliflower with 2 tablespoons of olive oil (or enough to lightly coat) on a large parchment lined rimmed metal baking sheet.
Roast for 20 minutes, then flip and carefully fold in the diced apple, adding more oil if necessary.
Roast another 20 minutes, or until the cauliflower and apple are tender and golden.
Meanwhile, add the remaining 1 tablespoon of oil to a medium-large pot over medium heat.
Add the shallot, then reduce the heat to medium low, cooking for 15 minutes, or until very soft, stirring occasionally.
Add the dried thyme then cook 1 more minute.
Add the vegetable broth then cover and bring to a boil.
Carefully add the diced potatoes to the boiling broth, then cover and cook 10 to 15 minutes, or until completely tender.
Add the roasted cauliflower and apple to the pot, along with the nutritional yeast and lemon juice.
Blend with a hand blender until smooth.
Season with salt and pepper to taste.
