Adjust oven rack to upper-middle position and heat oven to 450 degrees. Melt 1 tablespoon butter in Dutch oven over medium-high heat. Cook onion until softened, about 3 minutes. Stir in garlic and cook until fragrant, about 30 seconds. Stir in 2 cups cream, 1 cup broth, Yukon Golds, nutmeg, 2 teaspoons salt, and 1 teaspoon pepper. Bring to boil, then reduce heat to medium and simmer until potatoes are translucent at edges and mixture is slightly thickened, about 10 minutes. Off heat, stir in lemon zest and juice.
2. Transfer potato mixture to 13- by 9-inch baking dish and bake until bubbling around edges and surface is just golden, about 20 minutes. Meanwhile, melt remaining butter in large nonstick skillet over medium-high heat. Cook shredded potatoes until beginning to brown, about 2 minutes. Add remaining cream, remaining broth, and 1/2 teaspoon pepper to skillet and cook, stirring occasionally, until liquid has evaporated, about 3 minutes. Off heat, stir in 1/2 cup cheese and 2 tablespoons chives.
3. Remove baking dish from oven and top with shredded potato mixture. Sprinkle with remaining cheese and continue to bake until top is golden brown, about 20 minutes. Let cool 15 minutes. Sprinkle with remaining chives. Serve.
Make Ahead: The recipe can be made through step 1. cooled completely, transferred to the baking dish, and refrigerated, covered with plastic wrap, for 1 day. To serve, proceed as directed in step 2, increasing baking time to 25 to 30 minutes.