In a large pot, combine the water, onions, celery, lemons, jalapenos, garlic head, thyme, bay leaves, and Crab Boil. Season the water with salt and pepper. Bring the liquid up to a boil. Add the blue crabs and cook for about 15 minutes. Remove the crabs from the water and cool in a bowl of ice water. Cool the crabs for about 5 minutes and remove from the water. In a saucepan, combine the green onions, garlic, and chicken stock.
Season with salt and pepper. Bring the liquid up to a simmer. Cook the liquid for 10 minutes. Remove the sauce from the heat. Using a hand-held blender, puree the sauce until smooth. Strain the sauce through a fine mesh strainer. Reseason with salt and pepper if needed. Pile the crabs on a platter and serve with the dipping sauce.