Put the flours and salt in a large bowl, add the butter and rub into the flour between your thumbs and fingertips until the mixture resembles coarse breadcrumbs. Mix the lemon juice and water, pour over the flour and butter mixture and stir in quickly with a round-ended knife. When the dough starts to cling together, discard the knife and use the fingers of both hands to press the mixture gently together into a ball. Knead the dough lightly by pressing and turning it in the bowl until fairly smooth, then place it on a sheet of plastic wrap, press it into a disc and wrap tightly to exclude the air. Rest the dough for 20 minutes in the refrigerator before rolling out.
Roll out the pastry to line a 23 cm, fluted, loose-bottomed flan tin. Brush the inside of the pastry case with the egg. Chill the pastry case while making the filling.
Preheat the oven to 200˚C. Grill the bacon lightly and chop. Place the bacon and cheese in the pastry case in layers. Beat the eggs, flour, nutmeg, cayenne, salt, cream, milk and melted butter together and pour over the bacon and cheese. Bake for 10 minutes, then reduce the heat to 180˚C and bake for a further 20 minutes, or until a knife comes out clean. To serve, cut the quiche into wedges.