Place potatoes in a saucepan, and cover with water; bring to a boil. Reduce heat, and simmer 30 minutes or until tender; drain, reserving 1/2 cup cooking liquid. Cool and peel potatoes; mash. Add reserved cooking liquid, buttermilk, 3/4 teaspoon salt, nutmeg, and 1/8 teaspoon pepper, and beat at medium speed of a mixer until smooth.
Melt butter in a medium nonstick skillet over medium-high heat. Add onion and garlic, and sauté 2 minutes. Add mushrooms and cook 2 minutes, without stirring. Cook until liquid almost evaporates (about 4 minutes), stirring frequently. Remove from heat, and stir in 1/4 teaspoon salt, 1/8 teaspoon pepper, and basil.
Preheat oven to 375°.
Spread one-third of potato mixture in bottom of an 8-inch square baking dish or 2-quart casserole dish coated with cooking spray. Spread half of the mushroom mixture over potato mixture; repeat layers, ending with potato mixture. Sprinkle top with cheese and paprika; drizzle with oil. Bake at 375° for 25 minutes.