In a small bowl, stir together the garlic and lemon juice. Let it sit for about 5 minutes so the garlic can mellow and infuse the lemon juice - it’s like a quick flavor bath.
Finely chop the anchovies on a cutting board. Sprinkle a pinch of salt over the top and use the side of your knife to mash and smear it into a rough paste. Don’t skip this step - it’s the secret to that rich, savory depth we all love in a great Caesar.
Add the anchovy paste into the bowl with the lemon-garlic mixture. Whisk in the mayo, Worcestershire, pepper, and a handful of grated Parmesan. Taste and tweak - add a little more lemon juice or salt if it needs balance.
Cover and chill until you’re ready to dress things up.
Preheat oven to 425°F (220°C) and position a rack in the center.
Cut the pumpkin in half, scoop out the seeds, and peel the skin. Cut the flesh into ¾ to 1-inch cubes, trying to keep them fairly uniform for even roasting.
Place the cubes in a large bowl. Drizzle with 1 tablespoon olive oil, season with salt and pepper, and toss until everything is coated.
Brush a 13" x 9" area of a bare metal baking sheet with the remaining 2 tablespoons of olive oil. Sprinkle the grated Parmesan evenly over the oiled area. Arrange the pumpkin slices on top of the cheese, packing them closely together so each piece rests on the Parmesan layer.
Bake for 20 to 25 minutes, or until the pumpkin is tender and the cheese underneath is golden and crisp. Let it cool on the baking sheet for 2 to 3 minutes, then use a thin metal spatula to gently lift the pumpkin with its crispy Parmesan base intact.
Place the chopped kale in a large bowl. Add 2 teaspoons of lemon juice and a pinch of salt. Using clean hands, massage the kale for a minute or two, until it softens, darkens in color, and becomes tender.
Drizzle in about ¼ cup of the dressing and toss to coat the kale. Add half of the roasted pumpkin and a handful of shaved Parmesan, then toss gently to combine.
Transfer the dressed kale to a serving bowl or platter. Arrange the remaining pumpkin and a generous sprinkle of shaved Parmesan over the top. Serve the rest of the dressing on the side for drizzling.