Preheat oven to 425°F with oven rack about 6 inches from heat. Heat 1 tablespoon of the olive oil in a 10-inch cast-iron skillet over medium-high. Add sausage. Cook, breaking up sausage into pieces with a wooden spoon, until golden brown and just cooked through, about 4 minutes. Remove sausage to a medium bowl with a slotted spoon; set aside. Do not wipe skillet clean.

Add sweet onion, poblano chile, red bell pepper, and ½ teaspoon of the salt to skillet. Cook over medium-high, stirring occasionally, until onion is tender and peppers have charred in spots, about 8 minutes. Remove with slotted spoon to bowl with sausage. Wipe skillet clean.

Heat remaining 2 tablespoons olive oil in skillet over medium-high. Add diced potatoes to skillet in an even layer. Cook, undisturbed, until browned on bottom, about 5 minutes. Add ½ teaspoon of the salt. Continue cooking, stirring occasionally, until golden brown and crispy on most sides, about 5 minutes. Remove from heat. Return sausage and pepper mixture to skillet, and add garlic powder. Stir to combine. Stir in ½ cup each of the Gruyère and Cheddar cheeses until just combined.

Whisk together eggs, cream, and remaining ½ teaspoon salt in a medium bowl. Pour over mixture in skillet, and tilt pan to allow eggs to distribute. Top with remaining ½ cup each Gruyère and Cheddar cheeses. Bake in preheated oven until eggs have set and cheeses have melted, about 8 minutes. Increase oven temperature to broil, and broil until cheeses have turned golden brown, 2 to 3 minutes. Remove; let stand 5 minutes. Sprinkle with chives. Slice and serve immediately.