How to Make It
Whisk together first 5 ingredients and 1 1/2 tsp. of the salt in a small bowl until sugar is completely dissolved; slowly whisk in olive oil until completely incorporated.
Trim and discard tough stems from collard greens; thinly slice leaves, and place in a large bowl. Sprinkle with remaining 1/2 tsp. salt, and gently massage into greens 1 to 2 minutes. (This helps tenderize them and remove any bitterness.) Pour off any liquid.
Add carrots, apple, and 2 tablespoons of the dressing to collards; stir gently to combine, and let stand 30 minutes. Add 1/4 cup of the dressing to slaw, and toss. Serve remaining dressing on the side.