Place oil in a soup pot or Dutch oven on medium-high heat. Add onion and cook until softened, 5 to 7 minutes, stirring occasionally (do not brown).

Meanwhile toast almonds until lightly browned in a small dry skillet on low heat, stirring occasionally; watch carefully because nuts burn easily. Coarsely chop cauliflower florets; add cauliflower to onions and toss to combine. Add toasted almonds (reserving about 1/4 cup to use as garnish) and thyme leaves; toss to combine. Add water to cover by 1 inch. Bring to a boil on high heat; reduce heat to medium or medium-low and simmer until cauliflower is tender but not mushy, about 10 to 12 minutes.

Puree in batches in blender (high-speed blender works best) or food processor, adding salt to taste in the process. Pour into bowls. Garnish each serving with a small drizzle of truffle oil and reserved toasted almonds.