Slice the tomatoes into rounds and lay them out on a clean tea towel or kitchen paper. Sprinkle with salt and let them sit for at least 10 minutes. This draws out excess moisture and intensifies the flavour.
Preheat your oven to 180°C fan/200c. Line a rectangular baking tray with parchment and unroll your puff pastry onto it.
Using a sharp knife, lightly score a 1–2 cm border around the edges of the pastry, being careful not to cut through. Prick the inner section of the pastry with a fork to prevent it from puffing up too much during baking.
In a small food processor or using a hand blender, blitz the anchovies with their oil, grated parmesan, lemon juice, and a few grinds of black pepper. Drizzle in a little olive oil until you get a smooth paste. Fold the anchovy paste into the crème fraîche until well combined.
Spread the anchovy crème fraîche mixture over the centre of the pastry, avoiding the border.
Gently layer the sliced, patted-dry tomatoes across the top. Season with black pepper and a drizzle of olive oil.
Brush the edges of the pastry with beaten egg for a glossy golden finish.
Bake in the preheated oven for around 15-20 minutes, or until the pastry is puffed and golden, and the tomatoes are roasted and slightly caramelised.
Let the tart cool slightly. Tear the burrata and gently place over the top. Finish with an extra drizzle of olive oil and a crack of black pepper.
The video below will help with this recipe.