Preheat the oven to 450°.  Cut across the top of each head of garlic to expose some of the garlic cloves.  Place the garlic, cut-side-up, on a small pieces of aluminum foil; drizzle with olive oil and sprinkle with salt and pepper.  Place the rosemary sprig on top and fold the foil around the garlic to enclose completely.  Place on a small baking sheet and bake for approximately 1 hour, until the cloves are golden brown and soft.   When cool enough to touch, squeeze the cloves out of the skins and discard the skins.

In the bowl of a food processor, combine all of the dressing ingredients, except the oregano.  Add 2 tablespoons of cool water.  Process until thickened and thoroughly combined.  Season to taste with salt and pepper.  Stir in the oregano, if using.

Preheat the oven to 400°.  Lay the bacon in a single layer on an aluminum-foiled lined baking sheet and bake until crispy, about 12 to 14 minutes.  Drain on paper towels.

Pour 2 tablespoons of bacon fat into a medium skillet and preheat over medium heat.  Sprinkle both sides of the chicken breasts with salt, pepper and the minced rosemary.  Cook the chicken until golden brown and cooked through, about 5 to 6 minutes per side.  Remove the chicken from the pan and allow to sit for 5 minutes before slicing.

Assemble the greens, green onions and tomatoes; top with the sliced chicken, bacon and avocado.  Drizzle the dressing on top.