For the pastry, combine the flour and salt in a large bowl. Use a box grater to coarsely grate the butter over the flour mixture. Toss butter through flour mixture. Use fingertips to rub butter into flour until the mixture resembles coarse breadcrumbs. Make a well in centre. Add 100ml cold water and stir until a dough just comes together, adding remaining water if necessary. Turn onto a lightly floured surface and knead until just smooth. Shape into a disc. Wrap in plastic wrap. Place in the fridge for at least 1 hour, or overnight, to rest.
Heat the oil in a large frying pan over medium-high heat. Add shallot. Cook, stirring occasionally, for 3 minutes or until light golden. Add the butter and mushrooms. Season. Cook, stirring occasionally, for 5 minutes or until golden. Add thyme and garlic. Cook for 1 minute or until aromatic. Remove from heat. Stir in vinegar. Transfer to a plate and set aside to cool completely.
Preheat oven to 200°C/180°C fan forced. Roll out pastry on baking paper lightly dusted with extra flour to a 30cm disc. Carefully transfer dough on paper to a large baking tray. Spread pâté over centre of pastry, leaving a 4cm border. Top with mushroom mixture. Fold edge over filling. Brush pastry with egg. Bake for 35 minutes or until golden and crisp. Set aside for 10 minutes to cool slightly.
Meanwhile, pat the beef dry with paper towel. Season well. Heat the remaining oil in a frying pan over medium-high heat. Cook beef, turning, for 10 minutes or until browned. Transfer to a lined tray. Bake, with tart, for 12-14 minutes for rare or until cooked to your liking. Set aside for 15 minutes to rest. Use a sharp knife to thinly slice beef.
Combine the crème fraîche, mustard, chives and water in a bowl. Season. Top tart with beef. Dollop with crème fraîche mixture. Sprinkle with remaining chives and season.
