1.Cut the top and bottom from the fennel bulbs and remove any tough or bruised outer layers. You will end up with a bulb about the size of your fist.
2.Slice the bulbs in half and cut lengthwise into 1/8-inch slices.
3.Chop the fennel greens and set aside.
4.Heat a large skillet over medium-high heat and add about 2 tablespoons olive oil. Caramelize the fennel in batches, spreading the slices out in the pan to encourage browning. Sprinkle each batch with a pinch of sugar.
5.Cook for 10-12 minutes, flipping every few minutes, until golden brown.
6.Remove the fennel from the pan and drain off any excess oil. Season with a squeeze of lemon juice.
1.Pour the cream, ground fennel seeds and sugar into a saucepan over medium heat. Bring to a simmer then turn off the heat and let the fennel seeds steep for 10 minutes.
2.In another bowl, whisk together egg yolks and the whole egg. Allow the cream mixture to cool a bit then slowly incorporate the steeped cream into the eggs, one ladle full at a time, whisking constantly.
3.Scoop the cream from the top of the pan – the fennel seeds will settle to the bottom of your saucepan and can be discarded after all the cream is removed.
4.Add a pinch of your reserved chopped fennel greens and stir to combine.
Prepare filo dough:
1.Defrost the filo dough in the refrigerator the night before making the tarts.