Step 1

Prepare the leeks by trimming off the root and the dark green ends. Cut the remaining white and light green part of the leeks on the bias into 2-inch chunks and rinse to remove any dirt or debris. If your leeks are particularly dirty, they may need to be soaked in a bowl of cold water for a few minutes before being scooped out, leaving the dirt at the bottom of the bowl.

Step 2

Peel and cut the carrots on the bias into 2-inch chunks as you did with the leeks.

Step 3

Place a large skillet paired with a tight-fitting lid over medium heat. Add the butter into the skillet along with the carrots and leeks and season with salt and pepper. Allow the vegetables to cook, stirring occasionally, until lightly caramelized, 5 to 6 minutes.

Step 4

Add the garlic, thyme and honey into the pan and cook for 30 seconds to 1 minute just to bring the flavors together and lightly cook the garlic.

Step 5

Carefully deglaze the pan with the white wine, scraping up any browned bits, then add in the broth. Cover the pan, reduce the heat to low and simmer until the leeks and carrots are tender, 25 to 30 minutes.

Step 6

Remove the lid, turn the heat up to high and bring to a boil. Continue to cook until the liquid has reduced by about half, 3 to 5 minutes. Remove the pan from the heat, scatter with the cheese and parsley and serve.