Preheat oven to 250 degrees. Place cornbread cubes onto a baking sheet. Drizzle with olive oil and sprinkle with salt. Toss to coat. Bake until dry and crispy, at least 1 hour.
Rinse and dry the Brussels sprouts. Using a knife, slice into thin strips. Alternately, shred them using the grater attachment of a food processor.
Bring a large pot of water to a boil. Prepare a large bowl of ice water. Drop the Brussels sprouts into the boiling water for 1-2 minutes. Then, immediately plunge them into the ice water for 1-2 minutes. Drain.
Make the dressing: Whisk the mustard, maple syrup and vinegar together. Whisking constantly, slowly pour in the vegetable oil. Stir in the rosemary.
Divide the Brussels sprouts, croutons, pecans, cranberries and cheese among 4 entree dishes. Drizzle with dressing and serve.