Prepare a charcoal grill by lighting charcoal and letting it burn until it glows bright orange, ashes over, and is very hot. Brush the grill grate generously with oil.
Meanwhile, put the ostrich meat in a mixing bowl, sprinkle generously with salt and pepper, and form into 4 equal-size patties about 3/4-inch thick. Grill the burgers, turning once, until medium-rare, about 3 minutes per side. Remove from the grill and let stand for 5 minutes.
Spread 1 tablespoon of the yogurt on each of 4 muffin halves, and 1 tablespoon mustard on each of the remaining muffin halves. Place the burgers on the mustard-coated muffins; top each with a slice of tomato, lettuce, and a generous pile of pickles. Top with the yogurt-coated muffins and serve immediately.
Prepare a hot fire in a charcoal grill or preheat a gas grill to high.
Put the cucumbers, cut-side down, on the hot grill and cook, without turning, until grill marks appear and the cucumbers have softened slightly, 2 to 3 minutes.
Meanwhile, whisk together the honey, vinegar, 1/3 cup water, the pickling spices, turmeric, chili flakes and garlic in a small bowl, glass jar or pie plate. Transfer the hot cucumbers to the pickling liquid, being sure they are completely submerged. Let stand for at least 15 minutes before draining and slicing crosswise. Pickles can be served immediately, or sliced and stored in the pickling liquid in the refrigerator for up to 1 week.