In a small bowl, combine lemon zest and juice, 2 teaspoons of the oil, the soy sauce, garlic, 2 teaspoons of the thyme, and the pepper; brush over mushroom caps.
Marinate at room temperature while preparing an outdoor grill with a medium-hot fire (or preheating a stove-top grill pan).
In a small bowl, combine tomatoes, chickpeas, vinegar, red onion, cheese, salt, pepper, remaining 2 teaspoons of the oil, and remaining thyme.
Grill bread slices 2 minutes per side, until lightly toasted.
Place on 4 plates.
Grill mushrooms, gill sides down, 4 minutes.
Turn caps over and fill with tomato mixture.
Cover grill; continue to grill 3 to 5 minutes (if making on grill pan, invert a large bowl over mushrooms), until mushrooms are just tender but still hold their shape.