Glazed Carrots with Braised Bibb Lettuce

Ingredients

• 16 carrots with tops (you can tell how fresh the carrots are by the tops), not more than 3/4 inch in diameter, peeled and trimmed with 1 inch of top left on
• 1 teaspoon sugar
• 1/2 teaspoon salt
• 1 1/2 teaspoon white wine vinegar
• 1 bay leaf
• 1 sprig fresh thyme
• 3 tablespoons unsalted butter
• 1 or more grinds of white pepper
• 6 Bibb lettuce leaves, larger ones torn in half