Combine the flour, cold butter cubes, salt and parmesan in a food processor and mix for 1-2 minutes. Add the cold water gradually and mix again until fine crumbs form.
Place the crumbs on a floured, cold surface and knead until it comes together as a dough. Form into a disc and cover the dough with plastic wrap. Chill in the fridge for 30 minutes.
for the fillings
Peel and slice the onions finely. Heat a tablespoon of oil in a frying pan on high heat. Add the onions and stir occasionally to prevent them from catching.
Once the onions have browned slightly reduce the heat to low and let slowly caramelise for 8-10 minutes. Season with salt and add a tablespoon of balsamic vinegar. Cook for two more minutes until well combined and set aside.
Trim the ends off the asparagus and cut the spears into three even parts. Cut the asparagus spears lengthwise in half, skip this step if the spears are very thin.
Heat a tablespoon of olive oil in a wide pan on high heat. Once the pan is hot, add the asparagus and roast stirring occasionally. Add the thyme sprigs and season with salt and pepper.
Roast for just 3-4 minutes leaving the asparagus still crunchy. Set aside on a plate to cool.
assembling the tart
Pre-heat the oven to 190°C (375°F). Roll out the dough into a large circle about 2-3mm thick. Place a large, round plate on the dough and cut off the broken edges.
Lift one side from the surface and fold if it feels fragile and crumbly place the dough in the fridge or freezer for a few minutes.
Spread the caramelised onions in a circle leaving a large border all around. Place the asparagus on top and spread out nicely. Fold the overlapping edges over the outer ring of the filling, pleating the dough naturally.
Brush the the dough with the beaten egg and sprinkle additional thyme over the dough and asparagus. Place on a baking tray and bake in the oven for 25 minutes.
Remove from the oven and let cool for 5 minutes. Be careful when lifting the dough as it can break easily. Serve the crostata with a salad and herbed labneh.