Prep the salad per the instructions above. Arrange the ingredients in a bowl.
Make the vinaigrette: Whisk together the ingredients for the vinaigrette with salt and pepper to taste. Set aside.
Make the pasta: Cook the pasta per the package directions, reserving 1/2 cup of the water before draining well.
Meanwhile, heat the broiler on low.
Melt the butter in a nonstick skillet on medium heat. Add garlic and cook, stirring, until fragrant, 1 to 2 minutes. Add sweet potato, heavy cream, salt, and nutmeg and simmer the mixture until slightly thickened, 3 to 5 minutes. Stir all but 1 tablespoon of Parmesan into the sauce to melt. Remove from heat, stir in the cooked pasta, and fold to coat in sauce, adding reserved pasta water 2 tablespoons at a time if too thick.
Meanwhile, make brown butter: Melt butter in a small saucepan on medium. Add hazelnuts, garlic, salt, and nutmeg and cook, stirring often, until butter browns and hazelnuts and garlic are golden, about 3 to 5 minutes. Once the butter browns, remove it from the heat immediately and transfer it to a small heatproof bowl. Then stir in the sage.
Transfer the pasta to a baking dish, sprinkle with remaining parmesan, and broil until golden brown around the edges, about 2 minutes.
Toast the bread and dress the salad.
Mix together the sparkling water and lemon. Serve over ice if desired.
Portion the pasta and top with hazelnut brown butter and chopped parsley. Enjoy with bread, salad, and spritzer.