Heat olive oil in a skillet over medium heat until shimmering, then add minced garlic and cook until fragrant and just starting to turn golden, about 1 minute. Transfer the garlic and oil to the slow cooker.
Add shredded rotisserie chicken and chopped roasted tomatoes to the slow cooker, along with ground cumin and a pinch of salt and pepper. Stir gently to combine the ingredients evenly.
Pour chicken broth into the slow cooker, then cover and cook on low for 4 hours, allowing the flavors to meld and the tomatoes to break down into a smoky, velvety base.
Once cooking is complete, carefully use an immersion blender or transfer to a blender to puree the tomato mixture until smooth, creating a vibrant, deep-colored broth that is rich in smoky flavor.
Return the pureed broth to the slow cooker, then add the tortellini. Cover and cook on high for another 15-20 minutes, until the tortellini is tender and plump with broth.
Use a microplane or fine grater to zest the lime directly into the soup, then squeeze in the lime juice, stirring gently to brighten the flavors. Add chopped cilantro on top for fresh, herbal aroma.
Taste the soup and adjust salt, pepper, or lime for balance. Serve hot, garnished with extra cilantro if desired and accompanied by crusty bread or tortilla chips for a satisfying meal.
