1. For Yogurt Cheese: Line a fine-mesh strainer with 3 basket-style paper coffee filters or a double layer of cheesecloth. Set the strainer over a deep container (there should be enough room for a generous 1/3 cup liquid to drain without touching the strainer). Spoon the yogurt into the strainer, cover tightly with plastic wrap, and refrigerate until the yogurt has released about 1/3 cup liquid and has a creamy, cream cheese-like texture, 10 to 12 hours (it can stay in the strainer for up to 2 days).
2. Transfer the yogurt cheese to a clean container, discarding the drained liquid, and cover with plastic wrap. (The cheese, covered, will keep for up to 1 week in the refrigerator.)
3. For Topping: Stir the peppers, sun-dried tomatoes, olives, vinegar, oil, and garlic together in a medium bowl and season with salt and pepper to taste. Cover with plastic wrap and let stand at room temperature until the flavors meld, about 1 hour. (The mixture, covered, can be refrigerated for up to 2 days. Bring to room temperature and season with additional sherry vinegar, salt and pepper as needed before serving.)
4. For Crostini: Adjust an oven rack to the middle position and heat the oven to 400 degrees. Arrange the bread slices in a single layer on a baking sheet. Bake until the bread is dry and crisp, 8 to 10 minutes, turning over the slices halfway through baking.
5. Remove the toasts from the oven and, while still hot, rub one side of each toast with the raw garlic clove. Spray with the olive oil and sprinkle liberally with salt and pepper. (The toasts are best topped and served shortly after they come out of the oven, but you can set the toasts themselves aside for several hours and top just before serving.)
6. When ready to serve, spread a thin layer of yogurt cheese over each crostini, top with about 1 tablespoon of the pepper mixture, and serve.