Pre-heat the oven to 160ºC/Gas Mark 3 and place a baking tray inside to heat up.
Whisk together the eggs and crème fraîche until smooth, season with salt and pepper then set aside.
Heat the olive oil in a frying pan and cook the shallots over a low heat, stirring often, until softened and golden. Set aside to cool.
Blanch the asparagus and peas in a pan of boiling water for 2-3 minutes then drain and tip into a bowl of iced water.
To prepare the tart base, stir together the melted butter and olive oil. Unwrap the filo pastry and lay between two damp tea towels to prevent it drying out as you work.
Brush a 20cm loose bottomed tin with the butter and oil mixture then lay a sheet of pastry into the tin, sticking it to the sides. Don’t worry if it doesn’t cover the whole surface, you can cover any gaps with the next sheet of pastry. Brush with more butter and oil then repeat the layers until you have used all the pastry. Use scissors to trim the pastry into an even edge just above the tin. You may find it best to cut the pastry sheets in half to better fit your tin.
Stir the cooled shallots, peas and artichokes into the egg mixture then tip into the tart case. Lay the asparagus on top then sprinkle over the Parmesan.
Slide the tin onto the hot baking tray in the oven and bake for 30 minutes or until the filling is just set. Leave to cool in the tin.
Serve with pea shoots and a drizzle of lemon oil.