Flank steak is the perfect candidate for cooking under the broiler. The high heat sears it on the outside while leaving the inside juicy. If you can't find flank, strip steak or hanger steak would work well, too.
Position racks in upper and lower thirds of oven; preheat to 425°F. Line a rimmed baking sheet with foil.
Toss carrots and onion with 1 tablespoon oil and 1/4 teaspoon each salt and pepper on an unlined large rimmed baking sheet. Roast on the lower rack until soft but not browned, about 10 minutes. Remove from oven. Increase oven temperature to high broil.
Meanwhile, combine 1 tablespoon each oil and honey, tamarind, tamari (or soy sauce) and 3/4 teaspoon cumin in a small bowl. Reserve half for serving. Place steak on the prepared baking sheet and sprinkle with the remaining 1/4 teaspoon each salt and pepper. Brush one side with the tamarind mixture.
Broil the steak on the top rack, flipping once and basting with the tamarind mixture, until an instant-read thermometer inserted in the thickest part registers 145°F for medium, 8 to 10 minutes total. Transfer the steak to a clean cutting board and let rest for 5 minutes.
Whisk vinegar, the remaining 1 tablespoon oil, 1 1/2 teaspoons honey and 1/4 teaspoon cumin in a large bowl. Stir in the carrots and onion, dates and mint.
Slice the steak across the grain. Drizzle with the reserved tamarind sauce and serve with the vegetables.