Place a 10-inch cast-iron skillet on the center rack of oven, and preheat oven to 375°F.
Meanwhile, place eggs, sour cream, cornmeal, flour, sugar, baking powder, salt, granulated garlic, and 2 ½ cups corn kernels in a blender. Process until smooth, about 30 seconds. Transfer to a large bowl; stir in 1 cup cheddar cheese and remaining 1 cup corn kernels until well combined.
Carefully remove skillet from oven; add butter, swirling skillet until butter is melted. Working quickly, pour batter into hot skillet. (Do not stir.) Top with jalapeño slices and remaining ½ cup cheddar.
Bake until edges are lightly browned and pudding is fully set (an instant-read thermometer inserted into center of pudding should read 165°F), about 35 minutes. Let stand for 10 minutes before serving.
