Preheat the oven to 190C/375F/Gas 5.
For the almond purée, in a medium-sized pan melt the butter and sweat the chopped shallots until soft and transparent. Season with salt, to taste.
Add the milk and almonds and bring to the boil. Cook for 30 minutes.
Place the almonds and shallots into a blender with a few tablespoons of the milk they have been cooked in. Blend to make a fine purée. Adjust the consistency by adding more cooking liquid if required and a dash of cream and almond oil to taste.
Return the purée to a smaller pan, season with salt and freshly ground black pepper and keep hot.
For the trout, melt the butter with the olive oil in a non-stick, ovenproof pan. Heat until the butter is foaming. Season the trout with salt and freshly ground black pepper before placing them into the pan. Cook for approximately three minutes on the first side before carefully turning the trout over and transferring the pan to the oven for ten minutes.
Remove the pan from the oven. Squeeze the lemon juice over the trout and leave to rest for a few minutes.
To serve, spoon some of the hot almond purée onto each serving plate before placing the fish onto the plate. Add the parsley to the warm cooking oil in the pan, stir, then spoon over and around the fish.