Preheat oven to 450°F. Remove green leaves from cauliflower and reserve. Cut cauliflower heads in half, then into bite-size florets. Cut stalks into bite-size pieces also. Place florets and stalk pieces in a roasting pan, drizzle with olive oil and season with salt and pepper. Roast until golden and tender, about 20 minutes. Transfer to a platter lined with paper towels to drain.
Pour 1⁄4 inch of oil into a small saucepan. Add the garlic and set the pan over medium heat. Heat the oil until the chips are golden and crisp, about 1 minute. Drain on paper towels and set aside.
Set a large skillet over medium-high heat. Add the olive oil and fry the anchovies, garlic, capers and thyme, stirring with a wooden spoon to break up the anchovies and infuse the oil. Cook for 3 to 4 minutes, until fragrant. Add the cream and Parmesan, and bring to a simmer. Just before serving, add the roasted cauliflower pieces and fold in the reserved leaves.
Finish with a squeeze of lemon juice, and top with the fried garlic chips, cracked black pepper and shaved Parmigiano-Reggiano.
Reprinted from Tyler Florence Fresh (2012, Clarkson Potter, a division of Random House)