Warm the oil in a large skillet over medium heat.
Soften onion and jalapeño, stirring, 3–4 minutes.
Stir in garlic, cumin, and oregano; cook until fragrant, 30 seconds.
Add zucchini; cook, stirring, until edges begin to brown, 4–5 minutes.
Pour in broth, then fold in corn and tomatoes.
Simmer until zucchini is tender and liquids reduce, 5–7 minutes.
Stir in lime juice and cilantro; season with salt and pepper.
Sprinkle cheese over the top; cover to melt for 1 minute, then serve.