Prep the Leeks: Trim the root end and tough dark green tops from the leeks. Slice them in half lengthwise and wash thoroughly under cold water to remove all grit. Pat dry and slice into 1/2-inch pieces.

Heat the Pan: In a large skillet over medium heat, melt the butter with the olive oil.

Sauté Aromatics: Add the minced garlic and sauté for about 30 seconds until fragrant.

Cook the Leeks: Add the sliced leeks and optional thyme sprig to the skillet. Season with salt and pepper and stir to coat.

Soften and Steam: Cook, stirring occasionally, for 5-7 minutes until the leeks begin to soften. Pour in the broth, bring to a simmer, then reduce the heat to low. Cover and cook for 5-8 minutes until tender.

Finish: Remove the lid, increase heat to medium-high, and cook for 1-2 minutes to evaporate any remaining liquid. Remove the thyme sprig, taste, and adjust seasoning before serving.