Heat your oven to 200°C/Fan 180°C/Gas 6. Tip the flour into a mixing bowl, saving a pinch for later. Finely grate in half of the cheddar. Chop in the cold butter. Use your fingers to rub the ingredients together until they resemble coarse breadcrumbs.
Crack the egg over a small bowl and carefully separate the yolk from the white. Stir the yolk into the flour mixture with 3-5 tbsp cold water, until you have a soft dough. Wrap in greaseproof paper or cling film and put in the fridge to rest for 15 mins. Keep the egg white for later.
Trim the root and any dry ends off the fennel, halve lengthways and thinly slice. Pour 1 tbsp oil into a frying pan and bring to a medium heat. Slide in the fennel and sprinkle in a little salt and pepper. Fry for 5-6 mins, till slightly softened and golden around the edges.
Meanwhile, halve the cherry tomatoes. Peel and thinly slice the garlic clove. Pick the rosemary leaves and roughly chop them. Coarsely grate the remaining cheddar.
Lay the pastry on a sheet of greaseproof paper. Roll out into a rough circle a little larger than a dinner plate, using the reserved flour to dust your rolling pin if needed. Slide onto a flat baking tray.
Sprinkle the reserved cheddar evenly over the pastry, leaving a gap of 3cm around the sides. Arrange the cooked fennel on top. Scatter on the cherry tomato halves, cut-side up, and tuck in the sliced garlic, rosemary and olives. Sprinkle over a pinch of salt and pepper.
Carefully fold up the pastry edges over the outside edge of the filling. Brush the pastry with the remaining egg white. Slide the tart into the oven and bake for 35 mins, till the pastry is golden brown and cooked through.
While the tart is baking, squeeze the lemon juice into a small bowl. Pour in 1 tbsp oil and add a little salt and pepper. Whisk together well to make a dressing. When the tart is nearly ready, tip the peppery salad leaves into a bowl and toss with the lemony dressing. Serve with thick slices of the tomato, fennel and olive tart.