In a large deep skillet, melt the butter over medium heat. Add the carrots, onion, garlic, bay leaf and 1 tbsp. thyme; season. Cook, stirring occasionally, until the carrots and onions begin to soften, about 5 minutes.
Stir in the peas and lettuce. Cook, stirring often, until the lettuce begins to wilt and the peas are heated through, about 4 minutes. Discard the bay leaf. Sprinkle with the remaining 1 tbsp. thyme. Serve immediately.