Heat oven to 375°F. 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.
Heat half & half, chicken broth, butter, garlic, mustard, and salt in saucepan over medium-low heat until smooth, about 5 minutes. Keep warm.
Drain potatoes and transfer to bowl of stand mixer fitted with paddle and mix on medium-low speed, slowly adding half-and-half, until smooth, about 1 minute. Beat in eggs one at a time for about 1 minute. Add in chives.
Transfer potato mixture to greased 2-quart baking dish and use fork to make peaked design on top. Bake until potatoes rise and begin to brown, about 35 minutes. Let cool for 10 minutes. Serve.