In a large Dutch oven, heat canola oil over medium-high heat. Add onion and garlic; cook, stirring occasionally, until translucent, approximately 6 minutes. Stir in carrot; cook until tender, approximately 10 minutes.
Stir in broth, turkey, salsa, hominy, tomatoes, cilantro, bay leaves, cumin, oregano, pepper, and lime zest. Bring to a simmer; lower heat to medium-low.
Cover and cook 1 hour to 1 hour and 30 minutes. Remove cilantro and lime zest strip; discard. Season with salt, if desired. Garnish as desired.
Recipe by Louisiana Cookin' at https://louisianacookin.com/turkey-posole/