Separate the egg yolks from egg whites.

Make sure the butter and coconut oil are softened, best at room temperature.

This will make it easier for you to bind with the egg yolks.

 *UPDATE: An easier way that always results in smooth ice-cream is to place all the ingredients in a food processor and pulse until smooth.

Then pour in an ice-cream maker and process according to the manufacturer's instructions.

To get powdered Erythritol, simply place it in a food processor and pulse for about 15-20 seconds.

If you use whole Erythritol, it will not dissolve and will create unwanted crunchy texture.

Slowly add the egg yolks and whole eggs while blending one by one...

...

and process until smooth.

Pour in the coconut milk and keep blending.

It's likely the mixture will lump which is perfectly normal.

This is when using a food processor instead of a mixer becomes handy.

Scoop the mixture into the ice-cream maker and process according to the manufacturer's instructions.

Half way through, remove from the ice-cream maker.

Use an immersion blender and pulse until smooth.

Then, return to the ice-cream maker and continue until your ice-cream is done.

If you notice lumps, pulse with the immersion blender again.

Eat immediately or place in the freezer for 30-60 minutes if too soft.