Whisk together the goat cheese and milk until smooth in a medium bowl.
Combine the carrots, vinegar, butter, honey, 3/4 cup water, and 1/4 teaspoon each salt and pepper in a large skillet. Cook, covered, over medium-high heat until crisp-tender, 8 to 10 minutes. Uncover and cook, stirring occasionally, until all the liquid has evaporated and the carrots begin to caramelize, 2 to 3 minutes. Remove from heat, add 1 tablespoon water, and toss until the carrots are coated with the glaze.
Meanwhile, heat the oil in a separate large skillet over medium-high heat. Season the steaks with 1/2 teaspoon salt and 1/4 teaspoon pepper. Cook until an instant-read thermometer inserted into the thickest steak registers 130° F, 2 to 4 minutes per side for medium-rare. Let rest for 5 minutes; thinly slice against the grain.
Serve the steak with the carrots and the whipped goat cheese, sprinkled with the chives.
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