Preheat the oven to 400°F / 200°C and line a large baking sheet with parchment paper.
Chop the cauliflower including the core pieces. Spread the cauliflower on the baking sheet and toss with a drizzle of olive oil and pinches of salt and pepper. Wrap the shallot and garlic cloves, along with a drizzle of olive oil and a pinch of salt, in a piece of aluminum foil and place it on the baking sheet with the vegetables. Roast them for 30 to 35 minutes or until the cauliflower is browned around the edges.
In a large pot or Dutch oven, bring the vegetable broth to a simmer over medium heat. Add the roasted cauliflower, shallots, peeled garlic, and thyme and simmer covered with lid for 15 minutes.
Let it cool slightly and transfer to a blender. Add the miso paste, mustard, 3 tablespoons of olive oil, and the lemon juice. Blend until it becomes smooth.
Season to taste with ¼ to ½ teaspoon more salt and more lemon juice and serve.
