Begin by heating the oil in a large pot over medium heat. Add the diced onion and sauté for 5 to 6 minutes until it becomes soft and translucent. Stir in the crushed garlic and cook for another minute, making sure it doesn’t brown.
Add the corn kernels and cook for about 5 minutes, stirring often, to lightly caramelize. Pour in the broth and bring everything to a gentle simmer. Let it cook uncovered for about 10 minutes, until the corn is tender and the flavors are well combined.
Remove the pot from the heat and allow the mixture to cool slightly. Transfer about two-thirds of the soup to a blender and blend until smooth. Then return it to the pot and stir to combine, so you get a creamy base with some whole corn kernels for texture.
Add the Greek yogurt, Cotija cheese, and lime juice. Stir well and return the pot to low heat, warming the soup gently for 2 to 3 minutes without boiling, to avoid curdling the yogurt.
Taste and adjust seasoning if needed. Serve hot, topped with extra Cotija cheese, a sprinkle of chili powder, chopped cilantro, or a dash of hot sauce, if desired.