Preheat the oven to 400°F (200°C).
Melt 1 tablespoon of butter in a large heavy skillet over medium-high heat.
Add the corn, 1/2 teaspoon salt, and a pinch of black pepper to the skillet and cook, stirring occasionally, until the kernels are deep golden brown, about 5 minutes; transfer to a mixing bowl.
Melt the remaining 1 tablespoon of butter in the same skillet over medium heat.
Add the finely chopped yellow onion and red bell pepper and cook, stirring often, until the onions are wilted, about 2 minutes.
Add the chopped green onions, minced jalapeño, and minced garlic and cook, stirring, until the vegetables are softened, about 2 minutes; transfer to the bowl with the corn.
Stir in the mayonnaise, a pinch of cayenne, half of the shredded cheddar, and half of the shredded Monterey Jack until evenly combined.
Spoon the mixture into an 8-inch square or similar 1–2 quart baking dish and sprinkle the remaining cheddar and Monterey Jack evenly over the top.
Bake until the dip is bubbly and the cheese is golden brown on top, about 20 minutes.
Remove from the oven and serve hot with tortilla chips.