In a medium saucepan, cover beans with cold water by 2 inches. Add one quarter each of onions, and jalapenos and bring to a boil over high heat. Reduce to a rapid simmer, cook until beans are tender, 45 to 50 minutes.
In a large Dutch oven or heavy pot, heat oil over medium-high heat. Add garlic and remaining onion, season with salt and pepper. Cook, stirring often, until onions are soft and golden brown, about 10 minutes. Stir in remaining jalapenos, cumin, beans with their cooking liquid, and broth. Season with salt & pepper. Bring to a simmer and cook until beans are soft, about 10-20 minutes (if necessary, add more broth to keep beans covered).
Transfer 2 cups soup to a blender and add corn starch. Puree until smooth (use caution when blending hot liquids). Return to pot. Cook, stirring until soup thickens, 1 to 2 minutes. Add fresh lime juice and season to taste with salt and pepper. To serve, top with diced avocados, onions, tomatoes, cilantro, yogurt, and tortilla strips if desired.
Cook's Note: To make tortilla strips, cut corn tortillas into thin strips, toss with a little oil, then bake at 350 degrees until crisp.