Preheat broiler to high.
Combine yogurt, olive oil, 1/4 teaspoon pepper, and 1/8 teaspoon salt.
Cut each flatbread in half at the fold. Broil 1 minute or until toasted, turning after 30 seconds.
Cut cucumber in half lengthwise. Place cut side down, and cut into 1/4-inch slices.
Heat a nonstick skillet over medium-high heat. Add ground beef to pan, stirring to crumble. Add tomatoes to pan; cook 6 minutes. Stir in remaining 1/2 teaspoon pepper and remaining 1/8 teaspoon salt.
Spread 1 tablespoon yogurt mixture on each flatbread half; divide beef mixture evenly among flatbreads. Top evenly with cucumber slices and remaining yogurt mixture.
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