Preheat the oven to 250˚ F. Combine the potatoes, milk, 1/2 teaspoon salt and a few grinds of pepper in a medium saucepan and bring to a boil. Reduce the heat and simmer until the potatoes are fork-tender, about 10 minutes. Remove to a bowl with a slotted spoon; reserve the milk.
Meanwhile, heat 3/4 inch vegetable oil in a large cast-iron skillet over medium-high heat until a deep-fry thermometer registers 375˚ F. Whisk 1 1/2 cups flour with 1 tablespoon chili powder in a shallow bowl. Whisk the buttermilk, egg, remaining 1 tablespoon chili powder and a pinch of salt in a separate bowl. Season the steaks with salt and pepper. Coat the steaks in the flour, dip in the buttermilk, then coat in the flour again.
Working in batches, fry the steaks, turning once, until crisp and golden, 5 minutes; transfer to a rack set on a baking sheet. Season with salt and keep warm in the oven. Reserve the cooking oil.
Put the peas and carrots in a microwave-safe bowl and add 2 tablespoons water; cover and microwave until hot, 4 minutes. Mix 3 tablespoons of the reserved cooking oil and the remaining 1/4 cup flour in a bowl with a fork. Return the milk to a boil, whisk in the flour mixture and cook, whisking, until thickened, 1 to 2 minutes. Season with salt and pepper. Reduce the heat to low and add the potatoes; warm through, 1 minute. Serve the steak with the potatoes and peas and carrots. Top with more gravy and chopped chives.