In a 4- to 5-quart pan over medium-high heat, combine 1/4 cup broth, onion, and garlic. Cover and stir occasionally until onion is limp, 5 to 6 minutes.
Add chili, cumin, and oregano; stir about 30 seconds. Add remaining broth, cover, and bring to boiling over high heat.
Meanwhile, cut carrots diagonally into about 1/4-inch-thick slices. Cut potatoes into 1/2-inch cubes. Cut beans into 2-inch lengths.
Add carrots and potatoes to pan; cover. When boiling, reduce heat to medium-low and simmer 10 minutes.
Turn heat to high, uncover, add beans, and when boiling, reduce heat to medium-low. Simmer until vegetables are tender to bite, 5 to 7 minutes.
Ladle into bowls. Add cheese, sour cream, tortilla strips, salt, and pepper to taste.
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