Preheat the oven to 400°F (200°C). Lightly grease a 12-cup muffin pan or line the cups with paper liners. If using canned corn, drain it well and pat it dry to prevent excess moisture in the batter.
In a large mixing bowl, whisk together the cornmeal, all-purpose flour, sugar, baking powder, salt, cumin, and chili powder. Break up any lumps so the leavening and seasonings are evenly distributed.
In a separate bowl, whisk the eggs, buttermilk, and vegetable oil or melted butter until smooth. If using melted butter, make sure it has cooled slightly before adding it to the eggs.
Stir the shredded cheese, corn kernels, diced jalapeños, and chopped green onions into the wet mixture. Distribute the ingredients evenly so each muffin gets a good amount of corn, cheese, and pepper.
Pour the wet mixture into the bowl of dry ingredients. Fold gently with a spatula until just combined. The batter should be thick, and a few small lumps are fine. Avoid overmixing, which can make the muffins tough.
Divide the batter evenly among the 12 prepared muffin cups, filling each about three-quarters full. If desired, sprinkle a little extra shredded cheese over the tops for a golden, cheesy finish.
Bake for 18–22 minutes, or until the tops are lightly golden and a toothpick inserted into the center comes out clean or with a few moist crumbs. Let the muffins rest in the pan for about 5 minutes before removing them.
Transfer the muffins to a wire rack and allow them to cool slightly. Serve warm with butter, sour cream, salsa, or your favorite soup or chili. Store any leftovers once completely cooled.