Heat 3 tablespoons of the olive oil in a medium-size skillet. Add the onion, red pepper flakes, and 2/3 of the chopped rosemary. Cook, stirring, until the onions are soft. Add half of the minced garlic and the olives and cook, stirring, for 1 minute. Remove from heat and cool.
In a small saucepan, combine 3 tablespoons of the olive oil, the remaining minced garlic and rosemary over low heat and heat through. Remove from the heat and set aside.
In bowl of an electric mixer with a paddle attachment, stir together the yeast, sugar and water. Add 2 cups of flour and beat on medium-low speed for 4 minutes. Let sponge sit for 30 minutes or up to 2 hours. Return the bowl to the electric mixer with dough hook attachment. Add the remaining flour, the salt and vinegar. Knead on medium-low speed for 5 minutes, or until the dough is very elastic. Add more flour if dough feels sticky. Place the dough in an oiled bowl and turn to coat with oil. Cover the bowl with plastic wrap and let rise until doubled in size. Punch dough and form into a ball. Turn the dough onto a floured surface and roll into 1/2-inch rectangle. Spread the onion mixture evenly on the dough and roll up tightly like a jellyroll. Press the roll out with a rolling pin to form a 10 by 12-inch rectangle. Gently stretch the dough onto an oiled baking sheet, making sure not to tear it.
With a pastry brush, coat the top of the dough with the rosemary oil and sprinkle with coarse salt. Let focaccia rise until doubled, about 30 to 45 minutes. Preheat oven to 425 degrees. Bake for 30 minutes, or until golden brown. Once cooled, cut into 8 even squares and set aside.
Preheat the oven to 350 degrees. In medium-sized bowl, place chicken and coat with 1/4 cup of the olive oil and thyme. Let sit for a few minutes. In small saucepan, combine the butter, pepper sauce, Worcestershire, wine and basil and simmer over low heat. In a medium-size skillet, add the remaining olive oil. Cook the onion and sugar together until lightly caramelized, and set aside. In a hot grill pan or on an outdoor grill, cook the chicken to mark on both sides, about 2 minutes per side. Coat lightly with the hot sauce and place the chicken on a baking sheet. Top each breast with roasted red pepper strips, cooked onions and a slice of cheese. Bake in the oven until cooked through, 10 to 15 minutes. Mix the honey and Dijon together. To assemble the sandwich, coat each slice of focaccia with mustard mixture. Place a chicken breast on focaccia slice and cover with another bread slice. Cut sandwich in half wedges.
Yield: 4 sandwiches