Preheat oven to 450°F. Bring vinegar and 1/3 cup water to a simmer in a small pot. Remove from heat. Add raisins, cover, and let sit until ready to use.
Divide squash, thyme, and garlic between 2 rimmed baking sheets; arrange in a single layer. Toss with 2 Tbsp. oil, 1/2 tsp. salt, and 1/2 tsp. pepper. Roast 12 minutes. Toss, then add hazelnuts to 1 section of 1 sheet. Continue to roast until hazelnuts are toasted and browned and squash is tender and cooked through, about 6 minutes more.
Whisk ricotta and cream in a medium bowl until smooth. Add 6 oz. mozzarella, 3/4 tsp. salt, and remaining 1/2 tsp. pepper and whisk to combine. Remove thyme leaves from stems and add to cheese mixture. Coarsely chop garlic, add to cheese mixture, and stir to combine.
Transfer hazelnuts to a large bowl. Add panko, 2 Tbsp. oil, and remaining 1/2 tsp. salt and toss to combine. Set aside 1/4 cup panko mixture.
Drain raisins. Add kale, squash, and raisins to remaining panko mixture in large bowl and toss to combine.
Grease 2-qt. baking dish with oil. Add half of squash mixture, then dollop with half of cheese mixture. Top with remaining squash mixture, then dollop with remaining cheese mixture. Top with remaining 2 oz. mozzarella and reserved 1/4 cup panko.
Bake casserole until mozzarella is melted and browned in spots and edges are bubbling, 12–15 minutes. Let cool slightly before serving.