Place a grill pan over medium-high heat or preheat a gas or charcoal grill.
Using a pastry brush, brush the bread on both sides with 1/3 cup oil. Using a 1 3/4-inch round cookie cutter, cut out 4 circles from each slice of bread. Grill the bread rounds until toasted, 1 to 2 minutes each side.
Toss the eggplant rounds with the remaining 1 tablespoon oil and season with the salt. Grill until tender, about 3 minutes on each side.
In a small bowl, mix together the goat cheese and lemon zest until smooth. Spread about 3/4 teaspoon of the mixture on 8 grilled bread rounds. Place an eggplant round on each and top with a sun-dried tomato. Repeat the layers and top with the remaining bread slices. Gently press the layers together. Secure with toothpicks and serve.