1. Adjust oven rack to upper-middle position and heat oven to 375 degrees. Bring potatoes and water to cover by 1 inch to boil in large pot over high heat. Reduce heat to medium and simmer until potatoes are tender, about 20 minutes.
2. Heat half-and-half, broth, butter, garlic, mustard, and salt in saucepan over medium-low heat until smooth, about 5 minutes. Keep warm.
3. Drain potatoes and transfer to large bowl. With electric mixer on medium-low speed, beat potatoes, slowly adding half-and-half mixture, until smooth and creamy, about 1 minute. Scrape down bowl; beat in eggs 1 at a time until incorporated, about 1 minute. Fold in chives.
4.Transfer potato mixture to greased 2-quart baking dish. Bake until potatoes rise and begin to brown, about 35 minutes. Let cool 10 minutes. Serve.
5. Make Ahead: The baking dish with the potatoes can be covered with plastic and refrigerated for up to 24 hours. When ready to bake, let the casserole sit at room temperature for 1 hour. Increase baking time by 10 minutes.