Bring a pot of water to the boil and cook the broccolini until just tender - about 5 minutes. Drain and rinse in cold water. Set aside.
Preheat the oven to 200C (400F). Unroll the puff pastry but keep it on the paper it is wrapped in.
Place on a large baking tray and slice in in quarters or cut into four squres. Space the pieces slightly apart on the tray.
Score a small border around the edges of each piece with a knife and then prick within the border with a fork.
Bake for 8 minutes or until puffed and lightly golden.
Meanwhile, mix the goat's cheese, blue cheese or mascarpone and olive oil together in a bowl.
Press the middle of the galettes to flatten.
Gently spread a little of the cheese mixture around the inside border of each galette, leaving a space for the egg.
Crack the egs into a bowl and then gently slide into the galettes, being careful not to break the yolk.
Place the broccolini on the sides of each galette, over the cheese.
Sprinkle with the grated cheese, drizzle with a tiny amount of olive oil and season with salt and pepper.
Return to the oven for 12 minutes, tenting the galettes with foil after 6 minutes.
Check your galettes – the egg white should be just set. If the egg whites are still too runny then cook, uncovered, for a further 3 minutes. Remember that the egg will continue to cook slightly when you take the galettes out of the oven due to the residual heat.
Cool for 3-4 minutes then serve.
To make Croque Madame galettes, follow the recipe until step 5. Fill the edges of each galette with grated Cheddar cheese and chopped ham, leaving a space for the eggs. Continue with the method to cook.