Mix water and yeast and let stand 15 minutes. Gradually pour in 2 cups of the flour and incorporate. Mix for about 1 minute to form a sponge. Let stand, covered for at least 1 hour up to 2 hours to create the sponge.
Put sponge in the bowl of an electric mixer. Using the dough hook, add flour 1/2 cup at a time to form dough. Remove from bowl and knead. Place in a clean oiled bowl and let rise, slowly, about 1 hour. Divide dough into 4 balls. Roll out into 6-inch circles.
Heat grill to high. Brush the dough with olive oil and season with pepper. Grill the bread for 2 1/2 to 3 minutes on each side. Remove from the grill and brush with more olive oil.
Combine shredded cucumbers, yogurt, garlic, cumin, and chopped dill in a medium bowl. Season with salt and pepper, to taste. Garnish with fresh dill sprigs.