Scrub carrots thoroughly (do not peel), rinse well, and drain. Using a mandoline or food processor, slice into 1/8-inch-thick rounds, discarding tops. Transfer to a colander set over a bowl. Toss with sugar and 1 teaspoon salt. Let stand 1 hour, then rinse under cold water; drain.
Toast cloves or coriander seeds in a nonreactive 3-quart pot over medium heat, shaking pan, until fragrant, about 1 minute. Carefully pour in water. Stir in vinegar, honey, and remaining 3 teaspoons salt. Bring to a boil; add carrots and cook, stirring, just until brine returns to a simmer, about 8 minutes.
Spoon carrots into 2 clean quart jars, using a slotted spoon, and pack them in snugly. Carefully pour or ladle enough brine over veggies to cover completely, leaving about 1/2 inch headspace. Wipe rims with a damp paper towel. Let cool to room temperature, about 1 hour.
Apply clean lids. Chill at least 24 hours before eating for best flavor. (Flavor improves with time.) Store in fridge up to 1 month.