Arrange a rack in the middle of the oven and heat the oven to 425°F.
Cut the florets and stem of 1 large head cauliflower into bite-sized (about 1-inch) pieces. Place on a rimmed baking sheet, drizzle with 2 tablespoons of the olive oil, season with 1 teaspoon of the kosher salt and 1/4 teaspoon of the black pepper, and toss to coat. Spread into an even layer.
Roast, tossing halfway through, until tender and caramelized at the edges, 20 to 25 minutes total. Meanwhile, dice 1 medium yellow onion and mince 2 garlic cloves. Strip the leaves from 1 small bunch fresh thyme until you have 1 tablespoon. Squeeze 1/2 small lemon to get 1 tablespoon juice.
Heat the remaining 2 tablespoons olive oil in a large pot over medium heat until shimmering. Add the onion and garlic and sauté until softened and translucent, 5 to 7 minutes. Remove the pot from the heat.
When the cauliflower is ready, reserve 4 florets for garnish. Transfer the remaining cauliflower to the pot. Add 1 box (32 ounces) low-sodium broth, half of the thyme leaves, the remaining 1 teaspoon kosher salt, and remaining 1/4 teaspoon black pepper. Stir to combine, then place over high heat and bring to a boil.
Reduce the heat to medium. Cover with the lid slightly ajar and simmer until the flavors meld and the cauliflower is very tender, about 15 minutes.
Remove from the heat and add the lemon juice. Use an immersion blender to blend directly in the pot until smooth. (Alternatively, blend in batches in a regular blender.) Taste and season with more kosher salt and black pepper as needed. Divide the soup between 4 bowls and garnish with the reserved roasted cauliflower florets and thyme leaves.