4 cups fresh corn kernels (from about 6 ears), divided
2 large eggs
1 1/2 cups half-and-half
About 1 tsp. coarse kosher salt
1/2 cup chopped roasted green chilies (see Notes)
1 cup crushed buttery salted crackers (such as Ritz Crackers or Carr's Croissant Crackers, crumbled), divided
4 tbsp. melted butter, divided
1/2 cup grated Monterey jack cheese or pepper jack cheese