Step 1

Position rack in upper third of oven; preheat broiler to high. Line a rimmed baking sheet with foil.

Step 2

Combine 1 tablespoon oil, coriander, cumin, thyme, 1/2 teaspoon salt and 1/4 teaspoon pepper in a small bowl. Brush both sides of steak with the seasoned oil. Place on the prepared baking sheet. Toss onion with the remaining 1 tablespoon oil and the remaining 1/4 teaspoon pepper in a bowl and scatter around the steak.

Step 3

Broil, turning the steak and stirring the onion halfway through, until an instant-read thermometer inserted in the thickest part of the steak registers 145 degrees F and the onion is charred, 10 to 15 minutes.

Step 4

Meanwhile, combine water, vinegar, sugar and the remaining 1/2 teaspoon salt in a medium saucepan. Bring to a boil. Add vegetables and cook for 1 minute. Remove from heat.

Step 5

Slice the steak and drain the vegetables. Serve in pita bread with the charred onion and tzatziki.