Heat the strawberries in a saucepan and let them simmer for 10-15 minutes, until they thicken. Let cool for 10-15 minutes and then puree in a blender until smooth. The resulting quantity should be about ½ cup or 120 ml, just enough for the recipe.
Let the puree cool until room temperature before using it for the cupcakes. You can store it in the fridge for up to a week.
Line a 12-cup muffin tin with paper cases. Preheat oven to 360º F/ 180º C.
In a small bowl combine flax seed meal and baking powder. Mix very well and set aside.
In a large bowl whisk together oil and xylitol until smooth. Gradually add eggs, vanilla, cream and strawberry puree. Whisk after each addition, until smooth.
At the end add the flax seed meal and the coconut flour. Mix gently with a rubber spatula until absorbed.
Use a tablespoon or an ice cream scoop to fill the cupcakes about ¾ full.
Bake for about 20 minutes or until the tops become golden brown and a toothpick inserted in the centre comes out clean.
Let the cupcakes cool until room temperature before frosting them.
In a large mixing bowl whisk together the powdered xylitol and cocoa powder. Make sure no lumps remain.
Add the soft butter and start beating with an electric mixer at a low speed. Little by little add the milk and gradually increase the speed. Beat for about 1-2 minutes until the frosting becomes soft and fluffy.
Use a piping bag and a large star or round tip (or no tip) to frost the cupcakes.
Store the cupcakes in the fridge for 2-3 days. You can also freeze them for up to 3 months.
You can use any low-carb sweetener for the cupcake batter, no matter of its consistency.
For the frosting you need a powdered sweetener, even if it is not xylitol. However avoid powdered stevia or any other sweetener that is very concentrated as it has to add volume to the frosting and not only taste. You need at least ½ cup sweetener for the frosting (if you use that quantity of stevia, the taste would not be nice).