Warm the garlic cloves in the olive oil over low heat until the garlic begins to brown. Discard the garlic & let the oil cool. Meanwhile whisk the yeast into the water & let proof for 10 minutes. Add the cooled olive oil. Stir in the salt, flour & herbs & mix well. Knead by hand for 6 to 8 minutes. Place dough into a lightly oiled bowl, cover & let rise until doubled.
Divide the dough in half & set each piece on an oiled 10 1/2" X 15 1/2" baking sheet Stretch the dough to cover as much of the sheet as possible. Cover & let it relax for 15 minutes. Dimple & stretch the dough some more. Let rise until it is puffy, about 50 minutes.
While it is risng, roast, peel & slice the peppers into thin strips. Saute the onions in the 1/4 c olive oil over very low heat for 20 to 25 minutes until they are soft & limp.
Preheat the oven to 400F. Lightly dip your fingers into the remaining olive oil & dimple the tops of the dough. Divide the vegetables evenly in half & distribute them over the focacce. Sprinkle with badil & salt Bake for 25 to 30 minutes until the dough is crispy on the edges.
Cool briefly & then remove from the sheets & let cool on racks. Serve at room temperature.