Preparation In a large cast-iron or heavy-bottom skillet over medium-high heat, heat the oil. Working in two batches, add the carrots, season with salt, and cook, stirring occasionally, until golden brown and crisp-tender, 10 to 12 minutes. Transfer the carrots to a plate. Add the garlic and scallion whites to the skillet and cook, stirring, until the garlic is golden brown, 1 to 2 minutes. Add the mirin and 1/4 cup water and bring to a boil. Cook until thickened and reduced by half, 1 to 2 minutes. Reduce the heat to medium-low, and add the miso, whisking until smooth. Add the butter, a few pieces at a time, whisking to incorporate into a thick sauce, 2 to 3 minutes. Stir in the vinegar. Return the carrots to the skillet and toss to coat with the glaze. Taste and adjust seasoning. Sprinkle with remaining scallion greens and serve.