Preheat the oven to 350°. Grease a 2-qt. baking dish.
Put 1 3/4 cups corn kernels in bowl of a food processor. Pulse until mixture is puréed but still a bit chunky, about 5 pulses. Set aside.
In a large bowl, whisk together eggs, half-and-half, and 1 tsp. salt. Add whole and puréed corn kernels, green chiles, 1/4 cup crackers, and 3 tbsp. melted butter. Stir to combine. Spoon mixture into prepared baking dish and scatter cheese over top.
In a small bowl, mix together remaining 3/4 cup cracker crumbs and 1 tbsp. melted butter. Sprinkle over cheese.
Bake pudding 45 to 50 minutes, or until puffed and golden brown. The edges should be a bit crusty and the center still a little jiggly. Serve hot.
Note: Nutritional analysis is per serving.