Melt the butter in a large, heavy-based saucepan set over a medium heat. Sweat the leek and carrot for 6-7 minutes, stirring occasionally, until starting to soften. Add the pearl barley and stir well to coat in the vegetables and butter. Cook for 1 minute, then cover with stock and bring to the boil.
Add the thyme sprig and the bay leaf. Reduce to a simmer and cook gently for 20-25 minutes until the pearl barley is soft and tender. Stir in the peas and cook for a further 2-3 minutes.
Adjust the seasoning if necessary, then discard the bay leaf and thyme sprig. Ladle into soup bowls and garnish each with some thyme leaves. Serve with the bread layered on a side plate.