Soak ancho chiles in the boiling soaking water for 15 minutes. Blend softened chiles with 1 cup soaking liquid, tomato sauce, broth, garlic, cumin and oregano until completely smooth; discard remaining soaking liquid.
Heat oil in a skillet over medium heat and soften onion for 5 minutes. Add turkey and salt and cook for 8 to 10 minutes, breaking the meat into fine crumbles, until 165°F; fold in drained black beans.
Butter a 6-quart slow cooker and spread 3/4 cup ancho sauce over the bottom. Divide dry lasagna sheets into three groups and break them to fit with only small overlaps.
Layer one group of noodles, one-third of the turkey-bean mixture, one-third of the remaining sauce and one-third of the Jack. Repeat twice, keeping all noodle edges covered.
Cover and cook on low for 3 to 3 1/2 hours, checking at 2 1/2 hours, until the center sheets are tender and the filling reaches 165°F.
Switch off, uncover and rest for 20 minutes. Cut into eight portions with a wide spatula; no tortilla substitution or separate pasta boil is needed.