In a food processor, pulse the corn into a chunky puree. Place in a medium bowl. Add the cheese, 1/2 cup breadcrumbs, chives, sour cream, chipotle chile, 1 tablespoon chipotle chiles in adobo, salt, and pepper. Stir until combined.
Form the mixture into small balls and then flatten into patties, each about 1 1/2 inches in diameter and 3/4-inch thick. Refrigerate for 30 minutes. Coat the patties in the remaining 1/2 cup breadcrumbs and drizzle with olive oil.
Place a grill pan over medium-high heat or preheat a gas or charcoal grill. Brush the patties with olive oil and grill until toasted, 4 to 5 minutes each side. Arrange the corn cakes on a platter and top with a dollop of crème fraîche.
