To make the carrots: Whisk together sugar, lemon juice, spices, salt, and oil in a large bowl until sugar is dissolved.
Halve carrots crosswise on a long diagonal, then, starting from diagonal ends, cut into 1/16-inch-thick slices using slicer. Cook carrots in a 4 to 5-quart pot of boiling salted water until crisp-tender, about 45 seconds. Drain well in a colander and immediately toss with dressing. Cool to room temperature, stirring occasionally, then marinate, covered and chilled, at least 4 hours.
To make the tapenade and assemble sandwiches: Pulse olives with capers, parsley, anchovy, zest, lemon juice, and pepper in a food processor until coarsely chopped, then scrape down the sides of the bowl with a rubber spatula. Pulsing motor, 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.