For the shortcrust pastry
For the filling
Make a well with the flour on the board and add a pinch of salt. Add the cold butter cut into pats into the centre and work the ingredients with your fingertips until the mixture is crumbly. Add cold water and knead quickly without warming the mixture. Make a ball, wrap it in film and let rest in the refrigerator at least half an hour.
Remove the woody lower part of the asparagus and parboil them in lightly salted water.
Put the quail eggs in a small pan with cold water, bring to a boil, and cook for 3-4 minutes. Drain the eggs, rinse with cold running water to stop the cooking, and peel them.
Pour the cream into a bowl, add the two eggs, the diced bacon, the grated Parmigiano Reggiano, the thyme, the salt and pepper, and use a whisk to beat it until the mixture is smooth.
Roll out the pastry with a rolling pin until it is thin.
Line a rectangular oven dish with baking paper (or butter and flour it) and the line it with the shortcrust pastry. Trim the edges with a knife. Use a fork to prick holes in the bottom of the pastry. Cover with baking paper and fill with dried beans for baking (or a weight) and bake for 20 minutes. Remove from the oven and arrange the asparagus and quail eggs cut in half and then pour the egg and cream mixture over it.
Bake for another 25 minutes or until golden brown on the surface. Remove from oven, take out of the dish, and let cool slightly. Slice and serve.