Caramelized onion & anchovy pie

For a 30cm baking tray We Need : For Crust : 2 cups of flour 1/2 cup cold butter +1 tablespoons of water 1 egg large size 1 egg yolk large size For Filling: 2 tablespoons of butter 2 tablespoons olive oil 2 large onions finely sliced 2 green thyme leaves if available 2 eggs 1/2 cup milk 1/2 cup heavy cream 2 dried tomatoes sliced 3 cans of anchovy Salt and pepper 1 cup of cheddar cheese 1/2 cup of mozzarella cheese 1/4 teaspoon of paprika powder 1/4 teaspoon of somak powder