Wipe New Mexico, pasilla, and small chilies clean with a damp cloth. Stem and seed chilies, then place in a bowl with hot water to cover. Let stand until chilies are pliable, 5 to 10 minutes.
Drain chilies, reserving liquid.
In a food processor or blender, whirl chilies, peanut butter, sesame seed, tortilla, onion, tomato paste, chocolate, anise seed, cinnamon, cloves, coriander, and broth until smoothly ground.
In a 5- to 6-quart pan (preferably nonstick) over medium-high heat, brown half of the turkey in 1 teaspoon oil, turning as needed, about 8 minutes. (With a regular pan, you may need a little more oil.) Pour into a bowl; repeat to cook remaining turkey in oil and pour into bowl.
Add chili mixture to pan. Stirring often, bring to a simmer over medium heat, then reduce heat and simmer, covered, 15 to 20 minutes to blend flavors; stir often.
Add turkey and any juices to sauce. Stir in about 1/2 cup reserved chili water to thin sauce. Season to taste with salt.