Preheat oven to 450 degrees F. Line a baking sheet with parchment paper and coat with cooking spray.

Remove any outer leaves from cauliflower, but leave stem intact. Place on a cutting board, stem-side down. Using a large chef's knife, cut into ½- to ¾-inch-thick slices. The center few slices should remain more or less intact, but the outer slices will crumble into smaller pieces. Cut any of the medium pieces into ½- to ¾-inch-thick flat shapes--it's the flat surfaces that roast the best. Place the large and medium pieces on the baking sheet with the cut surfaces touching the parchment paper; sprinkle the small pieces in any empty spots. Coat the cauliflower with cooking spray and season with ¼ teaspoon pepper and ⅛ teaspoon salt.

Roast the cauliflower, gently turning once halfway through, until browned and the stems feel tender when pierced with the tip of a knife, 25 to 35 minutes.

Meanwhile, heat oil in a large skillet over medium-high heat. Add mushrooms and the remaining ¼ teaspoon pepper and ⅛ teaspoon salt; cook, without stirring, until the mushrooms are golden brown on one side, about 3 minutes. Stir and continue cooking until they've released most of their liquid, 2 to 3 minutes more. Add shallot and cook, stirring, until fragrant, about 1 minute. Reduce heat to medium. Add sherry and cook, stirring, until evaporated, about 1 minute. Sprinkle flour over the mushrooms and stir to coat. Add broth and bring to a boil, stirring. Cook, stirring, until thickened and reduced slightly, 5 to 7 minutes. Stir in thyme.

Serve the cauliflower "steaks" and any additional florets with the gravy.