Heat the oven to 200C/fan 180C/gas 6. Put the onion in a frying pan with a little olive oil and cook until it is tender and turning golden. Add a splash of water to the pan and cover with a lid for the first few minutes to start it off. Once cooked, leave it to cool.
Unroll the puff pastry onto a baking sheet and score a ½ cm border around the edge. Make patterns around the border with a knife if you like. Add the cheddar to the onion, season well and tip everything onto the pastry. Spread it out to the border.
Cut the Little Gem into quarters, mix the parsley with a little olive oil and plenty of seasoning and brush them all over. Fry them until the lettuce just starts to turn golden at the edges, then arrange on the tart. Bake for 10 minutes, or until the pastry is puffed and starting to brown.