Heat olive oil in a frying pan over high heat. Add mushrooms. Cook, stirring often for 6 minutes or until liquid has evaporated. Set aside to cool completely. Drain any excess moisture from the mushrooms and transfer to a bowl.
Combine flour and salt and pepper in a large bowl. Whisk the milk and eggs in a jug with a fork until well combined. Pour into the flour mixture and stir gently until smooth. Add mushrooms, chives and parsley. Stir gently to combine.
Add enough oil to a large non-stick frying pan to cover the base. Heat over medium heat until hot. Drop heaped spoonfulls of mixture into pan. Cook for 2-3 minutes or until bubbles appear on the top surface. Turn fritters over carefully and cook a further 2-3 minutes or until golden and cooked through. Transfer to a plate, cover cover with a clean tea-towel to keep warm while cooking the remaining fritters.
Serve at room temperature topped with a dollop of tzatziki dip.