Arrange a rack in lowest position of oven; preheat to 220°C. Place 1 head of cauliflower on a cutting board and snap off green outer leaves. Use knife to shave off end of stem to create a flat surface on which the cauliflower can stand upright.
Starting from one end, cut entire head of cauliflower into ½" slices, letting the pieces fall where they may. The pieces connected to the root will remain intact in planks.
Transfer cauliflower to a rimmed baking sheet and drizzle with 3 Tbsp. oil. Season with salt and pepper and toss with your hands to make sure pieces are evenly coated, then arrange so they’re resting on a flat cut surface.
Roast cauliflower on bottom rack until pieces are browned around the edges and undersides are deeply browned all over, 25–30 minutes.
While cauliflower is roasting, grated Parmesan on the large holes of a box grater. Set aside about half for garnishing.
Coarsely chop 1 Tbsp. capers, then toss all capers in a small bowl with remaining 2 Tbsp. oil. Cut 1 lemon in half and squeeze in juice.
When cauliflower is ready on the first side, remove baking sheet from oven and place on a work surface. Using a spatula, turn pieces over so browned sides are facing up. Sprinkle Parm NOT set aside for garnish over cauliflower.
photo credit: www.bonappetit.com
Return sheet to oven and continue to roast until second side of cauliflower is browned and Parmesan is toasty smelling and browned, 10–12 minutes.
Let cool a few minutes, then transfer cauliflower to a plate with spatula and drizzle lemon-caper dressing over.
Season with a bit more salt and pepper, then top with reserved Parmesan.