To prepare dough, dissolve yeast in warm water in a large bowl. Lightly spoon flour into dry measuring cups; level with a knife. Add 3 1/2 cups flour, 3 tablespoons basil, 1 tablespoon oil, and 1 teaspoon salt; stir just until moist.
Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 10 minutes); add enough of remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands.
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size.
Punch dough down; cover and let rest 5 minutes. Divide dough in half. Working with 1 portion at a time (cover remaining dough to keep from drying), roll each half into a 10-inch circle on a pizza pan or baking sheet coated with cooking spray. Cover and let rise 30 minutes or until doubled in size.
Preheat oven to 425°.
To prepare tapenade, heat 1 tablespoon oil in a nonstick skillet over medium-low heat. Add garlic; cook 30 seconds. Add eggplant; cook 8 minutes or until tender, stirring occasionally. Place eggplant mixture in a food processor. Add 1 tablespoon oil, 2 tablespoons basil, and next 4 ingredients (basil through olives); pulse 1 minute, scraping sides of bowl once.
Uncover dough. Spread 1/4 cup tapenade over each focaccia. Arrange tomatoes evenly over tapenade. Spread remaining tapenade over tomatoes. Bake at 425° for 20 minutes or until crust is golden brown.