Heat a deep, heavy pot over medium-high heat and add bacon. Add 1/4 cup water; simmer until water evaporates. Lower heat to medium-low; cook bacon until golden brown. Drain rendered fat.
Add oil and stir in the sofrito, scraping up the golden crust on the bottom of the pot. Cook the water out of the sofrito and stir in tomato sauce and tomato paste. Add alcaparrado, cumin and bay leaves.
Add corn, broth, 1 cup water and calabaza. Partially cover pot and bring to a boil. Lower heat to medium-low and simmer for about 35 minutes or until squash is very soft. Stir occasionally. If stew is too thin, smash a few pieces of squash against the pot to thicken it. Remove the bay leaves.
Stir in crabmeat; heat on medium-low, covered, 5 minutes. Garnish with cilantro.