In a large Dutch oven, combine the potatoes, 1 tablespoon salt, bay leaves and garlic. Add enough cold water to cover by 2 inches then set over high and bring to a boil. Reduce to medium, then cook until the potatoes are tender, 20 to 25 minutes. Drain the potatoes, then return to the pot
In a small saucepan over medium-low, melt 6 tablespoons of the butter. Add the melted butter to the potatoes. Using a potato masher, mash until smooth. Stir in the half-and-half, horseradish and 3 tablespoons of the reserved horseradish liquid. Taste, then season with salt. Cover and set over low heat to keep warm
Return the saucepan to medium and add the remaining 4 tablespoons butter and the caraway and mustard seeds. Cook, gently swirling the pan, until butter is browned and seeds are fragrant and toasted, 2 to 3 minutes. Strain into a small glass measuring cup. Transfer the potatoes to a serving dish, then drizzle with the butter and garnish with chives.