Begin by making the pie crust. Place the butter and sugar in a bowl and beat until combined. Add the egg yolks and beat for 60 seconds or so, until fully combined. Add the flour, 1/2 cup at a time and beat to combine again until the dough comes together. Remove the dough from the bowl and shape it into a round disc. Wrap in plastic wrap and place in the fridge for 1 hour to firm up.
In the meantime, make the filling. Add the olive oil to a frying pan over medium-high heat. Once hot, add the shallot and cook until the shallot has softened and has begun to turn translucent. Add the spinach leaves and cook uncovered until the spinach has wilted, about 3-4 minutes. Stir the spinach mixture occasionally so that the spinach doesn't burn. Once the spinach has wilted, add the salt and pepper and set aside to cool completely.
Preheat the oven to 375 degrees F.
Remove the pie dough from the fridge and place it on a lightly floured surface. Use a rolling pin to roll the dough out into a circle, about 5 mm (1/4 inch) thick. Roll the dough onto the rolling pin then place in the center of a 9 inch tart pan that is 1 inch deep. Gently lay the dough into the pan, ensuring that it doesn't stretch or rip. If the dough does rip, just gently press it back together with your fingers. Once the dish has been filly lined with the dough, trim the excess from the top and pierce the bottom of the dough with the tines of a fork. This will allow the dough to stay nice a flat with no air bubbles.
Bake the pie dough, uncovered, in the center of the oven for 18-22 minutes, or until it has turned a light golden brown. Once cooked, set aside and let it fully cool before adding the filling.
To make the filling, place the egg whites and whole eggs into a medium sized bowl and beat until combined. Add the cooled spinach mixture and the cheese and mix to combine again. Pour the filling into the pie dough, just until it reaches the top of the crust. Carefully place in the center of the oven and bake for 20-25 minutes, or until the filling has set and is not jiggly.
Remove the quiche from the pan and let it cool for 10-15 minutes before slicing and serving! Enjoy!