Preheat the oven to 400°F and fit the crust into a 9-inch tart or pie pan, crimping the edges.
Prick the bottom, line with parchment and pie weights, and blind bake 15 minutes until the edges turn pale gold.
Remove the weights and bake 5 more minutes, then reduce the oven to 350°F.
Heat olive oil in a skillet over medium heat and cook the asparagus 3 minutes, until bright green.
Add the peas and spring onion, cook 2 more minutes, then set aside to cool slightly.
Whisk eggs, cream, milk, salt and pepper together until pale and fully blended.
Scatter half the Gruyere over the bottom of the baked crust.
Spread the cooked vegetables evenly over the cheese.
Pour the egg mixture slowly over the vegetables, then top with the remaining Gruyere and dill.
Bake 35 to 40 minutes, until the center is just set with a slight wobble and the top is lightly golden.
Cool on a wire rack at least 15 minutes before slicing, so the custard finishes setting.
Serve warm or at room temperature, in wedges.
Good to Know
Bake the quiche the day before, cool completely and store covered in the fridge; it slices cleaner cold and warms gently in a 300°F oven for 15 minutes.