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Slice the fennel into slices, but not too thick. Heat a grill pan and brush the slices of fennel on both sides with some olive oil.
Grill the fennel slices for 2 to 3 minutes on each side until grill marks appear. Mix the crème fraîche with an egg until it's smooth. Season with pepper and salt.
Spread a thin layer on top of each piece of puff pastry, but leave the outer edges clear.
Finish the fennel tarts with some grated cheese, don't cover the fennel itself too much.
Bake the tarts for about 10 to 15 minutes in a 180 degrees Celsius or 350 degrees Fahrenheit oven, or until golden brown.
Serve immediately or refrigerate while covered for one day tops. Enjoy!