Bring a large pot of water to a boil over high heat. Season heavily with salt. Cook cabbage wedges until crisp-tender but not falling apart, about 5 minutes. Transfer to a paper towel-lined baking sheet. Pulse bread cubes in a food processor until coarse crumbs form; transfer to a medium bowl. Add mustard powder and stir to coat.
Heat 3 tablespoons oil in a small skillet over medium heat. Add breadcrumbs; stir frequently until golden, 4-5 minutes. Season with salt and transfer to a paper towel-lined plate to cool.
Whisk 3 tablespoons oil, Dijon mustard, vinegar, and 1 tablespoon water in a small bowl. Season mustard vinaigrette with salt and pepper.
Heat 1 tablespoon oil in a large cast-iron or nonstick skillet over high heat until smoking. Working in 2 batches and adding remaining 1 tablespoon oil between batches, sear cabbage wedges until dark and crispy edges form on both cut sides, 3-4 minutes per side.
Cook sausages in a large skillet over medium heat until browned and cooked through (time will vary depending on variety and whether fresh or fully cooked).
Transfer cabbage to a platter; arrange sausages around. Scatter breadcrumbs and tarragon over. Serve mustard vinaigrette on the side.
Per serving: 530 calories, 45 g fat, 4 g fiber Nutritional analysis provided by Bon Appétit