Heat the stock and butter in a large frying pan until simmering, stirring to mix. Add the peas and cook for two minutes, then add the Little Gem lettuce and two of the tarragon sprigs. Cook for 3-4 minutes, or until the lettuce has wilted, taste and season with salt and pepper to taste. Remove from the heat.
Meanwhile toast the slices of bread either on a griddle pan, under a hot grill or in the toaster. Season with a pinch of salt and pepper on both sides.
Heat a large, wide shallow pan of water. Break an egg in a teacup or ramekin. Whisk the vinegar and a pinch of salt into the water and gently drop the egg into the swirling water. Poach for 3-4 minutes or until the white is set and the yolk still runny (or until cooked to your liking). Remove with a slotted spoon and pat dry. repeat with the remaining eggs.
Remove the tarragon sprigs from the peas. Serve the peas on the toasts with a poached egg on top. Season the egg with a pinch of salt and pepper and garnish everything with roughly torn leaves from the remaining sprig of tarragon. Serve immediately.