How to Make It
Heat oil in a medium stockpot over medium-high. Add onion; cook, stirring occasionally, until translucent, 4 to 5 minutes. Add eggplant; cook, stirring occasionally, until softened, 4 to 5 minutes. Add bell pepper, 1/2 cup tomatoes, and minced garlic to onion mixture; cook, stirring occasionally, until softened, 4 to 5 minutes.
Process remaining 1/2 cup tomatoes in a blender until smooth. Add pureed tomatoes, stock, vinegar, sugar, salt, and black pepper to onion mixture. Bring to a boil, stirring occasionally. Reduce heat to low; cover and simmer until mixture is the consistency of marmalade, about 20 minutes. Remove from heat; cool to room temperature, about 15 minutes. Stir in 1 tablespoon basil.
Rub zucchini slices with cut sides of garlic clove; discard garlic. Top each zucchini slice with 1 1/2 tablespoons ratatouille. Top evenly with goat cheese, and sprinkle with remaining 1 tablespoon basil. Serve at room temperature.