Reduce the Vichy pastilles to powder.
Peel and wash the carrots, cut them into 1 cm cubes and cook for 20 minutes in the honey and pastille powder. Let cool.
In a bowl, work the butter left at room temperature with the sugar, add the eggs, almond powder, milk and 2 drops of peppermint extract.
Add the flour, baking powder and carrots. Mix well by cutting and lifting.
In a cake mold previously buttered and lined with parchment paper, pour the batter.
Bake the cake between 40 and 45 minutes at 170°C. Remove from oven and let rest 2 hours before turning out.
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