In a medium saucepan over medium heat, melt butter. Add rosemary, and cook, stirring frequently and adjusting temperature as needed, to allow butter to get brown bits on the bottom. Cook until butter becomes a golden brown color and smells nutty, about 2-3 minutes. Turn off heat. Add honey, stirring until well combined. Stir in apple cider vinegar.

Pour about half the glaze (and all the rosemary sprigs) over the carrots, tossing to coat. Season with salt and pepper. Place in preheated oven and cook for about 25-30 minutes (cook time will vary based on carrot size), stirring halfway through. Remove from the oven.

Meanwhile, while the carrots cook, make the whipped feta. Combine a feta, greek yogurt, lemon zest and juice, and olive oil in a food process and blend until smooth and creamy. Season with salt and freshly ground pepper.

To serve, spread whipped feta on a serving dish. Add carrots. Drizzle remaining glaze over the top (may need to reheat glaze briefly if thickened too much while cooling), then serve.