Heat a large nonstick or cast-iron saucepan over medium-high heat. (If the saucepan is not nonstick, lightly coat with cooking spray.) Squeeze the sausage out of the casings into the skillet. Cook, breaking up the sausage with a wooden spoon, until cooked through and golden brown. Transfer the sausage to a bowl and set aside.

Reduce the heat to medium. Heat the olive oil in the saucepan, then add the onions. Cook until light golden brown, stirring occasionally, about 4 to 5 minutes. Add the garlic, thyme, and cook for 1 minute.

Add the cauliflower and stir until combined.

Add the broth, bring to a boil, then lower heat and simmer until the cauliflower is very tender, about 15 minutes.

Remove from the heat. Stir in the spinach until wilted.

Let the mixture cool for about 10 minutes.

Use an immersion blender to puree the soup until very smooth. Alternatively, process the soup in a blender in two batches, pausing periodically to release the steam from the blender.

Stir in the ¾ of the cooked sausage.

Ladle the soup into four bowls, then garnish with the remaining sausage. Serve.