Preheat grill to medium-high.
Mash garlic and salt on a cutting board with the side of a knife until it's a smooth paste. Mix the paste with 1 tablespoon oil in a small dish. Lightly brush the oil mixture over portobellos and then on one side of each slice of bread.
Combine red peppers, tomato, feta, olives, vinegar, oregano and the remaining 1 tablespoon oil in a medium bowl.
Grill the mushroom caps until tender, about 4 minutes per side; grill the bread until crisp, about 1 minute per side.
Toss salad greens with the red pepper mixture. Place the grilled mushrooms top-side down on 4 half-slices of the bread. Top with the salad mixture and the remaining bread.