Heat the oven to 425°F. Line a rimmed baking sheet with parchment for easy cleanup and set a medium soup pot nearby.
On the baking sheet, toss the cauliflower with 2 tbsp extra-virgin olive oil, kosher salt, and black pepper; reserve the remaining 2 tbsp oil for the pot. Spread in an even layer and roast until deeply browned at the edges and tender, 25–30 minutes, turning once; set aside a few browned florets for garnish.
Warm the reserved oil in the soup pot over medium heat. Add the yellow onion and garlic and cook, stirring, until translucent and sweet, 5–7 minutes. Add the thyme and bay leaf and cook 1 minute until fragrant.
Pour in the vegetable broth and bring to a simmer. Add the roasted cauliflower (except the reserved garnish) and simmer gently, 10–15 minutes, until the flavors meld and the stalk pieces are very soft.
Remove the thyme and bay leaf. Blend the soup until completely smooth and silky, using an immersion blender in the pot or a countertop blender in batches; return to the pot if needed. Stir in the heavy cream and lemon juice, then taste and adjust seasoning as needed; adjust consistency with a little hot soup if you prefer it thinner and warm through, 1–2 minutes.
Ladle into warm bowls, top with the reserved roasted florets and chives, and serve hot.