Marinate the flank steaks

Set aside 2 Tbs. of the parsley. Combine the remaining parsley with the mint, rosemary, and garlic in a food processor and pulse until finely chopped. Add the lemon juice, soy sauce, 1 tsp. salt, and 1 tsp. pepper and process until smooth. With the motor running, add the olive oil in a thin stream.

Put the steaks in a nonreactive baking dish large enough to hold them both. Pour the marinade over them and turn to coat. Cover and refrigerate for at least 4 hours or overnight, turning occasionally.

Make the sauce

Cut the cucumber in half lengthwise and remove the seed core. Cut each half crosswise into 1/8-inch-thinck half moons and toss with 1/2 tsp. salt in a medium bowl. Let sit for 10 minutes to release excess liquid. Rinse, drain, and pat dry.

In a medium bowl, combine the cucumber with the yogurt, garlic, cumin, lemon zest and juice, and cayenne. Stir in the olive oil and the reserved chopped parsley, and season to taste with salt and pepper. Refrigerate until ready to use. (The sauce can be made up to a day ahead.)

Grill the steaks

Remove the steaks from the refrigerator 1 hour prior to cooking.

Prepare a medium-high gas or charcoal grill fire. Clean and oil the grill grates.

Remove the flank steak from the marinade, wipe off any excess, and season generously with salt and pepper. Grill the steaks, covered, until grill marks form and the steaks have a nice brown sear, 5 to 6 minutes. Flip the steaks and continue grilling until grill marks form on the other side and the steak is cooked to medium rare (an instant-read thermometer inserted in the thickest part of a steak should read 135°F), 3 to 5 minutes more. Let rest 10 to 15 minutes.

Cut the flank steak across the grain and serve with the cucumber-yogurt sauce on the side. Store the leftover steak in an airtight container and refrigerate for up to 4 days.