Preheat oven to 400°.
To prepare gorditas, combine first 4 ingredients. Stir in water, 1 1/2 tablespoons oil, and chipotle chile. Turn out onto a lightly floured surface; roll dough to a 1/4-inch thickness. Cut with a sharp (1 1/2-inch) heart-shaped cookie cutter into 12 gorditas. Place gorditas on a baking sheet coated with cooking spray; discard any remaining dough. Bake at 400° for 8 minutes. Reserve 6 gorditas for another use; refrigerate in an airtight container for up to 1 week.
To prepare posole, heat 1 1/2 teaspoons oil in a Dutch oven over medium heat. Add onion and garlic; sauté 5 minutes. Combine turkey and 1 tablespoon adobo sauce, tossing well to coat. Add turkey mixture to pan; sauté 3 minutes. Combine 1/4 cup broth and 1 tablespoon flour. Add broth mixture, remaining broth, hominy, and poblano chiles to pan; bring to a boil. Reduce heat; simmer 15 minutes. Remove 2 1/2 cups posole for another use; refrigerate in an airtight container for up to 1 week, or freeze for up to 3 months.
Arrange 6 gorditas on top of posole in pan; cover and simmer 5 minutes. Spoon 1 1/4 cups posole into each of 2 bowls, and top each serving with 3 gorditas. Sprinkle with cilantro.