First, make the pastry. Pulse the flour, butter and a pinch of salt in a food processor to the consistency of breadcrumbs. With the motor running, steadily add the chilled water, stopping as soon as the dough comes together.
Remove the dough, knead it a couple of times, then wrap it in parchment and chill it in the fridge for at least 30 minutes. Remove the pastry from the fridge and allow it to come up to room temperature before rolling.Heat the oven to 180C/ 160C fan/gas mark 4.
Roll out the dough to about 3mm thick. Line your tart case with the pastry (I used a rectangular one, about 15 x 25cm, and 3-4cm deep), leaving an overhang. Prick the base, then line it with baking parchment and baking beans.
Bake ‘blind’ for 20 minutes, then remove the beans and paper, and return the case to the oven for 10-12 minutes, until just golden. Remove from the oven and trim the overhang. Set aside.
To make the filling, pod the beans and peas (you can leave any very small fresh pods whole – they can go in the tart like that, if you like) and snap away the woody stems from the asparagus spears.
Set a large frying pan over a medium heat and add the olive oil, followed by the asparagus. Season with salt and pepper and cook for 2 minutes, then add the spring onions, lettuce, peas and broad beans (whole or not).
Continue to cook for a few minutes until the lettuce has wilted down. You’ll need to toss the vegetables around the pan to help them on their way.
Add the tarragon, parsley and lovage leaves to the pan. Season the mixture again with plenty of salt and pepper, then spoon into the prepared tart case. Dot the goat’s cheese over the top.
Combine the whole eggs, egg yolks, milk and cream in a jug, season and mix well, then pour the mixture over the tart filling.
Carefully place the tart in the oven to bake for 30-35 minutes, until it has a mottled golden top and is slightly raised. Allow to rest for at least 20-30 minutes before serving.