Preheat the oven to 400 degrees F (200 degrees C). Place poblano peppers on a baking sheet.
Roast peppers in the preheated oven until slumped and charred, about 30 minutes. Remove from the oven and let cool slightly. Reduce the oven temperature to 350 degrees F (175 degrees C).
Remove stems, seeds, and charred skin from peppers; roughly chop flesh.
Grease a 1 1/2-quart baking dish.
Whisk milk, cream, sugar, flour, melted butter, eggs, and salt together in a bowl. Stir in corn, Cheddar cheese, and chopped poblanos. Pour mixture into the prepared baking dish.
Bake in the oven until set, slightly puffed on top, and golden around the edges, 45 minutes to 1 hour. Garnish with chopped chives.