How to Make It
Preheat the oven to 325°. In a bowl, cover the chipotle with hot water and let stand until softened, 30 minutes. Bake the halved apples cut side down on a rimmed baking sheet for 30 minutes, until tender. Let cool. Scoop the apple pulp into a food processor and discard the skins. Stem, seed and chop the chipotle; add it to the food processor and puree.
Meanwhile, spread the bread in a pie plate and bake the pieces for about 10 minutes, until golden.
In a saucepan, boil the hard cider with the vinegar, sugar and apple puree. Simmer, stirring, until reduced to 3/4 cup, 10 minutes. Remove from the heat and season with salt.
Light a grill. Grill the sausages over moderate heat, turning, until lightly charred on both sides and cooked through, 12 minutes. Transfer to a plate and tent with foil.
In a skillet, heat the oil until shimmering. Add the broccoli and season with salt. Cover and cook until browned, 2 minutes. Stir in the mustard, caraway, cider sauce and 1/2 cup of water and bring to a boil. Remove from the heat, stir in the butter and season with salt. Serve the sausages with the broccoli and sauce, garnishing with the bread crumbs and apple matchsticks.