Deviled Eggs and Pickled Beets

Preheat oven to 400 °F. Wrap beets in foil, crimping tightly to seal; place on a rimmed baking sheet. Roast until tender, 45-55 minutes. Let stand until cool enough to handle. Peel beets and cut into 1" slices. Transfer to a wide, shallow container. Bring vinegar, sugar, coriander seeds, mustard seeds, cloves, bay leaf, 1/4 teaspoon sea salt, and 1/2 cup water to a simmer in a small saucepan over medium heat. Simmer for 10 minutes; pour liquid over beets. Let cool to room temperature, then cover and refrigerate overnight, turning occasionally. Slice eggs lengthwise in half and spoon yolks into a bowl. Mash yolks with a fork, then stir in the mayonnaise. Press mixture through a strainer into a small bowl. Add 1 tablespoon strained beet-pickling juice, horseradish, and a pinch of salt. Spoon or pipe mixture into each egg white. Finely dice enough drained pickled beets to yield about 1/2 cup (reserve any remaining beets for another use). Garnish each egg with diced beets and chives.