Mix tomatoes, eggplant, onion, mint, basil, and garlic powder in a saucepan; bring to a boil. Reduce heat to medium-low and simmer until liquid has evaporated, about 45 minutes, stirring occasionally.
Remove from heat and cool to room temperature.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Arrange bread slices on a baking sheet.
Toast bread slices in the preheated oven until crisp, about 3 minutes per side.
Let cool slightly.
Spoon tomato mixture onto each toasted bread slice; sprinkle with goat cheese.
Broil in the preheated oven until goat cheese is lightly browned, about 4 minutes.