Boil a small pot of water and blanch the basil leaves for 15secs. Drain and cool in cold running water. Squeeze out the excess water. Place in a blender, season and blend whilst adding oil until you have a smooth puree. Add some water if needed.
Heat a frying pan over a medium-high heat and melt butter. Add mushrooms and sauté until tender. Add shallot and cook for 2mins, season.
Add peas and broad beans and sauté for 1min. Break each egg into the pan. Cook until set (2mins). Drizzle over basil puree and creme fraiche, and sprinkle with tomatoes.