In a small bowl, combine garlic and lemon juice. Let sit 5 minutes.

Meanwhile, on a cutting board, finely chop anchovies. Sprinkle ¼ tsp. salt on top and continue to chop, smashing anchovies with the flat edge of the blade, until a paste forms.

To bowl with garlic mixture, add mayonnaise, Worcestershire, pepper, and anchovy paste. Whisk until combined. Whisk in Parmesan, then add more salt or lemon juice, if needed.

Cover bowl and refrigerate until ready to use.

Arrange a rack in center of oven; preheat to 425°. Peel squash and cut off stem. Cut in half lengthwise, then slice crosswise into ½" arches. Cut each arch in half to yield 2 smaller pieces. Transfer squash to a large bowl. Add 1 Tbsp. oil; season with salt and pepper and toss to combine.

On a bare metal baking sheet, brush about a 13" x 9" area with remaining 2 Tbsp. oil. Sprinkle Parmesan over. Arrange squash on top, packing close together to fit on top of cheese.

Bake until squash is tender and cheese is crisp and browned on the bottom, 20 to 25 minutes. Let cool on sheet 2 to 3 minutes. Using a flexible metal spatula, scrape frico-ed squash from baking sheet.

In a large bowl, combine kale and 2 tsp. lemon juice; season with salt. Using clean hands, gently massage lemon and salt into kale until kale turns dark green and wilts slightly.

Add half of dressing (about ¼ c.) and toss to combine. Add half of squash and half of shaved Parmesan and toss again to combine.

Transfer dressed kale to a serving bowl. Top with remaining squash and shaved Parmesan. Serve with remaining dressing alongside.