Bring a large pot of salted water to a boil. Add carrots and cook for 4–5 minutes until nearly tender. Add green beans and cook both together for another 3–4 minutes, until crisp-tender and vibrant. Drain and transfer to an ice bath. Once cooled, drain and set aside.

In a 12-inch sauté pan or wide skillet, add 2 tablespoons cold water over low heat. Once warm (not boiling), begin whisking in 6 tablespoons of cold butter, one cube at a time. Let each piece melt and emulsify fully before adding the next. Keep the heat low to maintain a stable sauce.

Add thyme sprigs to the sauce and let steep for 1–2 minutes. Add the carrots and green beans, gently tossing to coat. Let them warm through for 2–3 minutes. Season with salt and pepper.

Push the vegetables to one side of the pan or make a space in the center. Whisk in the remaining 2 tablespoons of cold butter, allowing it to melt and blend smoothly into the sauce. Then gently toss everything together to coat.

Remove thyme sprigs if desired. Transfer vegetables to a serving platter and garnish with a pinch of lemon zest for a fresh finish.