Heat the olive oil over medium-high heat in a large saucepan. When hot, add the chile arbol, chile guajillo, Chile Pasilla, and chile ancho and saute, stirring for 1 to 2 minutes or until the oil begins to turn a bit orange from the chiles; remove them from the pot with a slotted spoon and set aside.
Add the garlic, fresh tomatoes, poblanos pepper, and onion, and cook over medium-low heat until the vegetables soften, occasionally stirring about 10 to 12 minutes. Return the chiles into the saucepan, add the crushed canned tomato, rinse the can with 2 cups of hot water, and add the water to the pan; season with chicken bouillon and sazon goya culantro y achiote, sugar, black pepper, and red pepper flakes to taste.
Bring to a boil and immediately reduce heat to low, stirring and constantly scraping the bottom of the pan.
Using an immersion or standard blender, process the mixture in batches until smooth enough for your taste. If using a standard blender, take care not to fill the jar more than half full per batch, leave the hole in the lid open, cover with a clean dishtowel to allow the heat to escape), and pour it back into the saucepan.
Add the disassembled or shredded turkey and bay leaves to the saucepan to help the sauce develop more flavor, and bring the sauce to a simmer and cook, occasionally stirring, until it has deepened in color and reduced slightly, about 30 to 45 minutes (if the sauce begins to scorch, lower the heat). The sauce is done when the sauce is thickened and no longer watery.
Taste and adjust the season with salt and pepper, if needed. Remove the bay leaves along with the turkey and set aside until the turkey is cool enough to handle. Shred into bite-size pieces using your hands or two forks, discard the bones, return the meat to the pot and stir to combine.