For the posset: Bring the cream and granulated sugar to the boil in a pan. Reduce the heat to a simmer and cook for 1 to 2 minutes. Add the lemon juice and mix thoroughly. Pass through a fine sieve and set aside to cool for 5 minutes.
Skim off any air bubbles from the surface and pour into 6 serving glasses. Transfer to the fridge until set, at least 2 hours.
For the biscotti: Preheat the oven to 325 degrees F and line a baking sheet with baking parchment.
Sift the flour, baking powder and salt together in a medium bowl. In a separate bowl, beat the butter and granulated sugar together until smooth and creamy. Add the eggs one at a time with a spoonful of the flour mixture each time (to prevent the mix from splitting). Sift in the remaining flour mixture and mix to combine. Fold in the toasted almonds and fennel seeds.
Lightly dust a work surface with flour and shape the dough into 2 fat sausage shapes. Place on the prepared baking sheet and slightly flatten the dough. Bake until pale golden-brown, 20 to 25 minutes. Remove from the oven and leave to cool for 10 minutes.
After 10 minutes, slice each loaf into 3/4-inch-thick slices and lay the biscuits out onto a wire rack that will fit in the oven. Place the rack into the oven until the biscuits are dried out, 5 minutes. Remove from the oven and immediately dust with confectioners' sugar. Leave to cool completely before serving with the lemon posset.
Double cream, which is similar to heavy cream and has a butterfat content of 48 percent, can be found in specialty stores.