Step 1

Place carrots in a large bowl, season generously with salt, and toss to coat. Let sit at least 10 minutes and up to 1 hour to soften slightly. Pour off any liquid that collects in bowl.

Step 2

Meanwhile, cut peel and white pith from oranges. Working your way around, cut citrus flesh off cores in lobes. Cut each lobe into large pieces and place in a medium bowl; set aside. Squeeze cores over a small bowl to extract any juice (you want 2 Tbsp.; discard or drink any extra). Discard cores. Whisk oil, lime juice, and vinegar into orange juice; season with salt.

Step 3

Pour half of dressing over carrots and let sit, tossing occasionally, until ready to serve. Set remaining dressing aside.

Step 4

Heat a small skillet, preferably cast iron, over medium-high. Cook dates, turning occasionally, until blackened in spots, about 3 minutes. Let cool; remove pits.

Step 5

Just before serving, pour off excess liquid from carrots and discard (carrots will have softened by now). Drizzle reserved dressing over carrots and toss to coat. Tear dates into bite-size pieces; add to carrots along with reserved oranges and toss to combine. Taste and season with more salt if needed. Top with tarragon.

Step 6

Do Ahead: Carrots can be tossed with dressing 1 day ahead. Cover and chill carrots and remaining dressing separately.