Heat grill to medium-high flame.
Whisk together all ingredients for the dressing.
Slice Portobello caps so that you have 2 mushroom caps.
Brush dressing on to Portobello mushrooms and whole tomatoes.
The key to grilling Portobello mushrooms is making sure the grates are clean and brushed with oil right before the mushrooms go on.
Grill Portobello caps and tomatoes for approximately 7 minutes on each side or until you reach desired doneness.
Slice grilled tomatoes into rounds carefully with a serrated knife.
Place one sliced mushroom cap on each of four plates, and top each with some basil leaves. Stack another mushroom and 1 mozzarella slice onto each. Layer more basil and top with sliced grilled tomato and garnish with basil chiffonade (thinly sliced basil).