Melt 1 tablespoon butter in a small saucepan over medium heat. Add the thyme, apples and leeks. Cook, stirring, until the leeks are wilted, about 5 minutes. Add the cider and sugar, bring to a simmer over low and cook until the apples are tender, 6 to 7 minutes. Increase the heat and cook until the liquid is reduced and the apples are glossy, 2 to 3 minutes. Stir in the horseradish; season with salt and pepper. Transfer to a small bowl to cool slightly.
Place 2 slices bread on a work surface. Spread with the apple-leek conserve, then layer each with 1 slice Cheddar, half of the chicken, another slice Cheddar and another slice bread.
Melt the remaining 1 tablespoon butter in a medium skillet over medium-low heat. Cook the sandwiches, pressing gently with a spatula, until the cheese is melted and the bread is golden, 2 to 3 minutes per side.