For carrots
2 tablespoons sugar
1 tablespoon fresh lemon juice
2 teaspoons sweet paprika
1 teaspoon ground cumin
1/2 teaspoon cinnamon
1/4 teaspoon cayenne
1 teaspoon salt
1/4 cup olive oil
1 bunch medium carrots, grated
For tapenade
1 1/4 cups green olives (6 to 7 oz) such as Cerignola or picholine, pitted
3 tablespoons drained bottled capers, rinsed
1/4 cup chopped fresh flat-leaf parsley
1 flat anchovy fillet, chopped
1 teaspoon finely grated fresh lemon zest
1 1/2 tablespoons fresh lemon, orange or lime juice
1/2 teaspoon black pepper
1/4 cup olive oil
For sandwiches
12 slices good-quality whole wheat sourdough bread
6 oz soft mild goat cheese (3/4 cup) at room temperature

Prepare carrots:
Whisk together sugar, lemon juice, spices, salt, and oil in a large bowl until sugar is dissolved.  Add grated carrots, then marinate, covered and chilled, at least 4 hours.  Make tapenade and assemble sandwiches:
Pulse olives with capers, parsley, anchovy, zest, lemon juice, and pepper in a food processor until coarsely chopped, add oil in a slow stream and continue to pulse until mixture is finely chopped (do not pulse to a paste).  Spread tapenade on 6 slices of bread and goat cheese on remaining 6 slices, then make sandwiches with carrots.