Heat the olive oil in a medium skillet over medium-high heat. Add the red onion and cook, stirring occasionally, until lightly browned, 6 to 8 minutes. Transfer to a cutting board and let cool slightly, then roughly chop.
Mix the ginger, cayenne and lime juice in a medium bowl, then stir in the onion, tomatoes and cilantro. Let sit at least 20 minutes at room temperature.
Preheat a grill to medium high. Brush the bread with olive oil and season with salt. Grill until warmed through and lightly charred, about 2 minutes per side; brush with more olive oil. Add 1/2 teaspoon salt to the tomato salad and toss. Spread the bread with yogurt and top with the tomato salad.